There are lots of dumb parts / flaws of the criteria (the arbitrary quad designation is an obvious one, the lack of clearly articulated criteria for selection/seeding, the significance of the short non-conference season is another as has been mentioned), but I think some of the complaints are off-base.
The NET, KenPom, Torvik, BPI, etc. are all power ratings that are optimized to be predictive based on efficiencies. The typically have gotten some criticism for ignoring W-L record, overvaluing margin of victory, ignoring head-to-head, etc. But they are designed to be predictive, and do a good job of that.
The tournament doesn't and never has been selected based on power ratings, but rather on resume, or results. (I do think picking the tournament based on power ratings would be pretty absurd in practice). Winning vs. losing is pretty much all that matters. The RPI used to do this, since W-L was literally all RPI cared about (along with location of game).
There were a bunch of flaws with the RPI and other similar systems, but the big one was that a team could play a game and go down in the rankings, no matter what, just because they were playing a bad team, so that was obviously dumb.
Using the NET to develop quads theoretically still rewards winning and losing but theoretically does a better job of evaluating strength of schedule, although the arbitrary cut-offs on the quad designations is a new, but seemingly obviously dumb, flaw in the system.
ESPN calculates "strength of record" (it's more commonly used in college football) that I think does a good job of combines the two and solves the quad problem (
https://www.espn.com/mens-college-basketball/bpi/_/view/resume).
The conference strength issue is a bit complicated, since it's not "biased," it's just noisy. Kenpom calculates a metric called "luck" which is basically the difference between your predictive power rating and expected W-L rating based on that power rating. Teams with more wins against their schedule than you would expect are "lucky," teams with fewer wins than expected are "unlucky." We rank as the 352nd most lucky team out of 362. Theoretically, luck explains the difference between how good teams are and how likely they are to get a tournament bid.
One of the issues is because the non-conference play is both so impactful, but also has a small sample size, is that you see a lot of correlation between the luck factor of teams in the same conference. That is, if a conference is, on aggregate, unlucky in their non-conference games, that flows through into all the teams for the whole season. I don't think it will shock anyone to see that it looks like overall, the ACC has been rated as pretty unlucky by kenpom (on top of just not being that good). FWIW, I'm not sure this is a new problem.