They have the Big East name & better basketball teams at this point, if you don't know this by now, you have not been paying attention.
I am not a PC fan. I'm a UConn fan #1, but if you haven't noticed, a lot of bad things have been happening to UConn lately (APR issues, Post Season ban, ACC Decline) . If you think recruits are not paying attention, then I don't know where you've been looking. Until UConn solidifies their league, it's a big negative to UConn. I don't like it, but it's reality. You can keep hanging your head over years past, but Big Time recruits do not play in the past. They want to play in a top league today.
The Catholic League may have better teams from top to bottom, but PC is still on the bottom. UConn is the top of their league (unless they get an invite to the ACC/B1G - and then they are still near the top). Nobody may be getting excited for some of the UConn matchups but you have to kidding if you think even PC - Butler is going to draw an audience.
Two of the things you mentioned are things of the past for future recruits and have no bearing on their recruitment (APR issues, Post Season ban). The ACC Decline is a negative.
A lot of good things have happened also. Ollie has a contract and the practice facility has broken ground. It's not hanging your head in the past, it's building on the past. Big Time recruits do care about practice facilities and head coaches and past stars saying, "this guy is great as a coach/teammate."