You have very good points on all of this accept for the highlighted areas.
First of all, you're being a tad ridiculous saying 17 seed and you know it.
Second, yes I'd say last year was partially because of bad luck. A team dares you to beat them from 3 and you get wide open looks all game but shoot almost half of your average for the year and probably your worst shooting performance of the season. Shoot their average and they win, and their average wasn't very good. That's bad luck. The rest of the reason as to why we lost is because we relied heavily on freshman guards. They got scared down the stretch and you could see it.
The year before that, the team Purdue lost to also beat the 2 seed Kentucky. That would suggest that it was a better team than their seed, however our star player had arguably his worst game of his career as a Boilermaker. I'd say that was a little bit of bad luck too.
The year before that, Purdue shit the bed.
That's it. 3 bad years.
From there it goes like this moving backwards in time:
1 seed Virginia
3 seed Texas Tech
1 seed Kansas
12 seed Little Rock (young Purdue team, went to 2 OT's)
8 seed Cincy
2 seed Kansas
11 seed VCU (final four team)
1 seed Duke
1 seed Connecticut
3 seed Xavier
1 seed Florida
That rounds out Purdue under Matt Painter. So this narrative that we always bomb to lower seeds is just that. A narrative. The last 3 years is an anomaly in a lot of ways (across the board, not just for Purdue). We've seen more teams advancing further in the tournament than years past and it's mostly due to Covid holdover players. Mid majors are getting older and more experienced and it's paid dividends in the tournament.
BTW it was by sheer bad luck that Purdue didn't make the F4. It took a minor miracle for Virginia to get the game to OT.