It's even worse now. ONE only really does the webcomic, and now the story is basically Murata's. There are constant redraws where keeping up with the manga isn't worth it. This post highlights all the issues in the manga now if you care to read.
Hard to say. In this day and age of seasonals I do think their impact as the Big 3 would be felt less. Honestly, Dragon Ball, in my opinion, is the only one of the weekly anime that really would have survived the seasonal format and just been as impactful. Well, actually, Pokemon too, if we go beyond Battle Shounen because that IP is so huge.
Obviously there wouldn't be filler, and there would be more chapters adapted per chapter. TYBW is like 6 chapters per episode, while OG Bleach is like 2 chapters per episode. One Piece now is one chapter per episode

. (Wit remake is going to look good, but that shyt is never catching up ever.) Although I do wonder how popular the Big 3's manga was when they started out.

. That probably has a big factor to this conversation.
I could see the argument that the anime quality could be better. But the impact the Big 3 def wouldn't have happened in a seasonal format.
Though considering how much I hear people talk about One Piece, it takes x episodes until the anime gets good. It makes me really skeptical it could survive. I do think Naruto & Bleach could still do solidly.