Not really the case: someone of the noble Background has access to putting their floating ASI (because they are still floating within the confines of the Background, the bonuses are not assigned) i to Intelligence if they so choose, doesn't guarantee they will be more Intelligent than someone who doesn't.
Yes really the case in any actually-relevant example, such as two Wizards.
Yes obviously a Fighter is not going to be more intelligent, but that's meaningless and irrelevant. If we're using the standard array, someone with INT in their background will be able to start with 17 INT, and someone without, only 15.
That's bad on both mechanical and conceptual levels. Conceptually those seem like very different numbers - mechanically they are significantly different (anyone coming to me with "it's only 5%!", no buddy, that's absolutely not how actual maths work, I'm just telling you that right now). And because of the way ASIs work, they cap will stay in place until you've had multiple opportunities to raise the the stat.
Further, what you're not getting is, they may have to essentially WASTE the +2/+1. For example. You want to play a Wizard, you want them to have backstory X. Backstory X dictates Background Y. Background Y offers you +STR, CHA or WIS. As a Wizard, you don't really want any of those much. But you must put the +2 in one of them and you must put the +1 in another.
Even a better scenario, like you have DEX, CON and CHA maybe, you have to go for suboptimal stats (probably +2 CON, +1 DEX or swapping them depending on breakpoints), rather than +2 INT.
You've got to waste more than the equivalent of an entire Feat just to get equal! That's bonkers!
And it's purely down to the whims of some clueless designer at WotC, given we voted for a different approach and they never playtested this one!
EDIT - Obviously in real play the inverse will happen, which is that people will simply select from the very narrow selection of backgrounds that don't make them throw stat points on the ground and set them on fire lol. Like whatever backgrounds offer +INT and either +DEX or CON, those will be like 95% of Wizards