Up to which rating is my strategy in the opening is applicable? I don't want to waste time on opening preparation. By this, I mean that I don't want to have to understand/memorize the moves or the typical plans in the middlegame. I just want to develop my pieces, castle the king, and connect the rooks. From there, I wish to wing it, try not to blunder anything, and look out for tactics. Is this enough to reach 2000ELO?
This is an opinion based question as there is no way to know.
For Bobby Fischer it might have been, but I met Bobby and know that he memorized all the openings.
Would it work for you?
My tournament experience says no.
These days there are too many people memorizing everything along with all the better training for tactics than when I learned.
Your more likely ceiling would be 1500, with possibly 1700 IF you were really good.
After that, positional play would start to be a factor and by 2000  most players would beat  you with traps, better/deeper tactics, or positional play.
And since they do know the openings they would come out of most of them with an edge in position as well as the initiative.  So just routine play would give them the edge to win if they were at 2000 already.  And if they do not beat you in the middle game with strategy then they will win in the endgame because they are far better than lower rated players at endgames.
If you want to make even uscf 2000 let alone ELO 2000 you will have to specialize in ONE opening for white and one for black and become so familiar with them that you do not need to memorize them as the moves will be obvious because you do understand them.  And you will have to be totally fluent with ALL tactical motifs and recognize them in different game settings.