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What's really annoying to me nowadays are all the damn prompts to accept cookies.

Thank the EU for that one.  Websites cannot collect your information without your permission, so they now ask if you want to accept cookies in the most annoying way possible so you just accept them taking your data.
I'm a front end web developer for a platform that offers mobile and desktop views. You're right that it's a direction things are going in. Two insights I can offer:
1) Designing mobile and web completely separately takes up a ton of time and resources and most web teams (ours included) have a giant to-do list of things to make so anything that saves time is favored. 
This includes designing layouts that are similar between each (heck we have some designs that just adjust layout based on screen size doesn't even bother explicitly checking for mobile vs not). So whatever layout is chosen it's really likely they'll be really similar.
2) When designing, we are told it's a good design principle to start designing for mobile first, then adjust to web. So yeah things look even more mobile esque these days.
No comment on your opinion really, I don't have a strong opinion on it myself personally. Just verifying that in my work experience mobile esque design is becoming more of a thing. >

This.  This entirely.
Sprinkle in the internet's tendency to be an echo chamber where trendiness matters more than uniqueness, and you get what you get.  Everything looks the same. >

I think mobile devices like tablets and phones have overtaken desktops to browse the web, so it's natural to accommodate this shift. That being said, good web designers create visual layouts for various screen sizes and orientations.
What's really annoying to me nowadays are all the damn prompts to accept cookies.