One of those things is not like the others.
Though I agree with your point - partially. One Sweet 16 wouldn't magically change the perception of the program in the national commentariat, but I do think it would change a lot in our own fanbase's perception of what's going on.
I assume you mean Houston was good and possibly under-seeded enough that not getting past them was not some sort of "slip-up" on our part? If so, I agree, but everybody gets a lucky "hot streak" game every once in a while (like Shannon going off vs. UCLA last year), and it would have been nice for that to be ours! If you mean that COVID was equally unlucky for everyone, I agree in theory but it especially hurt teams who were bursting (back) on to the scene that year, IMO ... it would have and should have been Rutgers' program-defining return to the NCAA Tournament, for example. And I think the 2020 team that beat Iowa to end the season was playing like a team that could win two in the Tourney.
Regardless, I do believe that it would do more than just reassure our fan base's psyche. I was in Vegas for the Sweet Sixteen weekend this year, and it was astonishing how many "casuals" get REALLY into the NCAA Tournament (yes, I know the betting in Vegas probably makes it a bit different, but I am talking about people at regular bars), and I think when they keep saying certain programs represented there, it does a lot to reinforce the perception that "that program is good." We have done so much of the legwork to earn the perception of a top 15 program again, but when the lights are brightest and the most people are watching, we have not been there. And I think that really hurts us. Whether or not one Sweet Sixteen fixes that is debatable, but having none no doubt hurts a lot.