If Evangelion didn't happen modern anime would be quite different in both positive and negative ways. I agree with your complaint though; while it worked for NGE it's a trope that really should die.
Problem is that when something becomes innovative or foundational in its field, it becomes difficult to get out from under its shadow for a few reasons:
(1) people see how successful it is and want to try to repeat that so they try to iterate on that,
(2) when you see something you like and get inspired by it, you tend to bring at least some of the baggage it carries with it,
(3) it might just exert that prominent a place on the field's 'psyche,' as such -- how do you get away from something that many feel is defining?
You have to create something different that has the same or more impact on people. And if you go in trying to do that you are probably going to fail unless you are some kind of a genius. And not even a genius is guaranteed to succeed.
I agree that it gets bothersome to only have a small number of tools or techniques available to tell a story, but until someone comes out with something that can supersede it we are probably stuck with it. Also, considering these things are made for Japanese audiences and they might have more awareness of international markets than they did before, they are still intended for Japanese consumption. Maybe this is what works for those markets.
Or maybe it's what people who fund these shows think will make money -- isn't that the reason why we have some creative inertia out of Hollywood (despite Americans frequently clamoring for more options)?
I do think it works at times for some characters, but there are definitely cases where it is egregious. These stand out when you have shows that fans frequently label as "train wrecks," because, in part, the poor implementation makes the show a failure at what it's trying to do.
I think the genre that I have most frequently found the weak MC most bothersome in is harems. Perhaps because harems provide cheap and easy drama on some level, they have become popular story devices. And I frequently find myself bothered by them when I see an MC and I know he hasn't earned
the attention of multiple girls, let alone one of them.