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Population really is the driver of power and economies. 

Say you want to open a business. Do you want to open it in a market with 300,000 customers or 300,000,000 customers? 
As a country, you want to have the largest population possible. If you lose too much population you lose your economic power. 
At a global scale, yes, a lot of innovation is driven by an educated populace, but it also stems from the unbelievably gigantic global market that creates demand for your products. 
Smartphones would not be as good as they are if it wouldn’t be a market of literally billions of customers. not to mention all the niche markets that would simply not be worth any investment into if there wasn’t enough of an international market for it. (the internet has enabled many of those markets in the first place by aggregating globally spread out customers into one neat virtual place.)

Age structure is hugely important. 

The last thing you want is a large amount of elders with only few people to run the economy. Unless you want 80 year olds to be working office jobs, You do not want 2 retired people for every working person. 
First, while people live longer, I would not consider a 70 year old today much more better capable of work than a 70 year old 50 years ago. It’s just that there’s a lot more of them now surviving until that age. 
Also while yes, people should be saving, most people don’t save as cash or investments. They choose to pay into pensions a set amount of money during their lifes and then get paid back later. That money isn’t saved by those institutions. It’s immediately payed out to the current retired, and when you retire, the youngsters’ money will come to you. If the ratio is too extreme, the working generation will have to burden the pensions. 
Gradual decline isn’t as bad, but for many developed countries, the decline is concerningly rapid.
Population decline by itself isn't a bad thing. The rate of population decline is what is worrying. 
I live in a country that had just under 4.8 million people 30 years ago. According to last year census, we are just above 3,8 million now. By the end of this century we will be perhaps below 2 million. Whatever your political views, the idea that that sort of population decline wont have negative effects on the country and society is completely delusional.
And we are not an exception. Developed countries around the planet are going to have rapid population decline in coming decades.

Innovation comes from a well educated population. Not from a large population. 

If you live on a planet that has a bunch of old people, instead of young people, that means that a greater proportion of money and resources that would have otherwise been spent on education or innovations now has to go towards medical care for the old. Which means less innovation. 
Also. All other things being equal, would a planet with a million people or 10 billion people have more innovation ? The answer is obviously 10 billion. Larger well educated population will have more innovation than a smaller well educated population. Didn't think that was controversial. >


All other things being equal, would a planet with a million people or 10 billion people have more innovation ? The answer is obviously 10 billion. Larger well educated population will have more innovation than a smaller well educated population. Didn't think that was controversial.

The controversial part is where you need to gamble on those 10 billion people always being able to find technology that will save the day. Because if they don't, we are doomed.
On the other hand, if the planet only had 1 million, carbon emissions would be drastically reduced beyond our wildest dreams, and there would be plenty of resources for all. >



On the other hand, if the planet only had 1 million, carbon emissions would be drastically reduced beyond our wildest dreams, and there would be plenty of resources for all.


As someone worried about carbon emissions, do you know what percentage of the atmosphere is carbon?  And what percentage is the ideal? >

It's not that there's a particular number that's ideal, and the problem is that we've stayed from that number. It's that it's changing so rapidly that it's snowballing faster than life in general, and human society specifically, can adapt on a large scale. If the global average temperature rose by 5°C over the next millennium, it probably wouldn't be too big a deal. But half that over the next 100 years is a very big deal.
I guess if i had to give you a direct answer, it would be approximately the amount that we've spent the last few millennia learning to live in. Decisions from that are fine as long as they happen slowly enough that we can adapt socially, and other species can adapt genetically, to the change. >

The atmosphere is currently 0.04% carbon.
Are you saying that 0.05% too much and 0.03% the ideal? Or is 0.04% the ideal?  What happens if it doubles and reaches 0.08%? Catastrophe? >

You're really glossing over the whole "lots of old people, very few young people" problem. >

Yeah, OP says “people should be saving money for retirement, so lots of old people being retired shouldn’t be a problem”
This is a fundamental misunderstanding of how the world and the economy works. It doesn’t matter how much money people have saved for retirement if there aren’t enough working people to make the stuff they need to buy with that money.
It isn’t like saving for retirement means you are saving cans of food to eat later, like you are a squirrel burying nuts for the winter. You are saving money that you hope to trade in the future to someone else for your food and basic needs. This will only work if there is someone to trade your money to; if society is full of old people who have saved up money for retirement and not very many young people to make the food and things, then you are just going to get rapid inflation as all these old retired people try to trade that money to a dwindling number of productive people.
If this is hard to understand, just imagine the extreme… what if ALL the people are old, and they have all saved a ton of money…. Who are they going to pay that money to? No one is making food, they are all sitting on their pile of money wanting to buy food. The money would be worthless. >

ALL the people won’t be, so such an extreme is absurd. reductio ad absurdum >

I wasn't claiming the extreme example would ever happen, I was trying to show why having fewer working age people would lead to problems by using a hypothetical case of having no working age people... sometimes it helps to see an abstract thing like that by imagining the extremes.
Also, that isn't what reductio ad absurdum means; it is a form of argument where you show that if your argument wasn't true, you would end up in an absurd situation. >

Your argument isn’t true, and you end up in a state of absurdity. >

That doesn’t follow at all. I was not arguing that we are in a world, or even headed to a world, where there are no working age people. That wasn’t my argument.
And even if my argument WAS absurd, it still isn’t a reductio ad absurdum. It isn’t something you say to counter an absurd argument. It is a logical argument where you point out that your own argument has to be the case or you reach a contradiction >

My argument is that not all people can ever all be old. If that isn’t true, we end up in your absurd situation. reductio ad absurdum >

you are still using RAA incorrectly, you have the implications mixed up. >

Well, how ‘bout we admit your premise (all old people) is absurd and entirely unhelpful in advancing any argument. >

no. I'm not even the person you originally started to object to, but their argument is clear.
The premise is "in an aging population, there will be demand for goods and services that outstrip our ability to supply it, which will result in inflation", with the (perhaps implicit) conclusion that "world population decline is a major problem."
They have used an extreme example for illustrative purposes in order to argue why the (far milder) premise holds, but that extreme example is not their actual premise.
If you want to refute their premise you need to engage with it as stated, explain why having only, say, 20-30% of the population (vs. current 50%)  in the working age bracket (25-65) would not lead to demand for goods/services outpacing supply and leading to inflation.