Of course it would have been difficult and unpopular - correct decisions are often difficult and unpopular, but still need to be made.
As for the lack of public outcry about Solich taking over: It was a done deal and people didn't want to publicly criticize Solich before he had even coached a game, but a lot of people had doubts about it being the right way to go.
And to be fair, absolutely nobody NU hired was going to keep pace with what TO had done - going 60-3 over his last five years. It's also entirely possible that Byrne might have hired someone that would have done far worse than Solich. But in the end NU got what most athletic programs get when they allow legendary coaches to hand-pick their successor - mediocre results. There are some exceptions - Judd Heathcote and Tom Izzo, for example - but they are few and far between.