In principle there's nothing wrong with offer sheets. In fact, it's a bit of a problem that GMs/owners have this gentlemen's agreement not to use them. That's what allows them to lowball RFAs, so that mid-level young players can't get a big payday. That in turn is why we see teams blow up their rosters to try and cram as many ELCs and RFAs as possible under the cap. If there were more offer sheets, the league would probably be a little better-balanced and young players would definitely have a lot more leverage to get paid what they have earned.
With Aho specifically, I don't think Canes fans at any problem at all with the AAV. The issues were:
1) Losing a year of term, which means in a few years we have to pay a higher premium for another year of his prime
2) The financial structure which was specifically meant to hurt our franchise financially
Fortunately Dundon was capable of covering the signing bonus, but even so... this led into the pandemic season and a bunch of people being laid off. Maybe that looks a little different if Dundon still has that cash in hand (but probably not, to be brutally honest). In any case, it's a bit like when Philly gave Weber a contract that was specifically meant to destabilize the Predators, just a few years after they nearly relocated. That's a shot below the belt from a fan perspective, threatening the stability of the actual franchise itself. That, more than the actual contract, is what pissed off Dundon and the fanbase.