The problem for a coach that comes out after every poor performance and says 'it's on me', is that people will end up believing it. I watch all of the Packers games and I don't believe McCarthy was the problem.
Just saying
Who/what do you feel is the problem? If you think its Rodgers fine. If you think its overall talent fine. I'm not trying to be a smart ***, I'm curious.
I feel that 1 person is rarely the problem so the question is do you think McCarthy was part of the problem? If you say no then you probably think it was a mistake to fire him and that's fine. If you say yes he was at least part of the problem then the question becomes how do you fix it? I guess the answer to that depends on who/what you think is the problem or the rest of the problem.
If you think its on McCarthy AND Rodgers you have to know that Rodgers isn't going anywhere for a while so McCarthy is the one to go. It may not seem fair but that's the way it is. The other option is to force them to work together and I'm not sure if that would work at this point. If you think its overall talent you may have a point. Give him time to work with the guys Gute brings in.
The bottom line is something is wrong with this team and something needed to be done. Was firing McCarthy the right move. I say yes because I think it was time to move on and bring in fresh ideas. Even if the new coach fails miserably the decision to move on from McCarthy will still be the right move. The new hire might be the wrong decision but IMO its is independent of the choice to move on from McCarthy.
To follow up on what Weeds and the OP said though I agree 100%. Mike McCarthy was good for the Green bay Packers and I wish him nothing but the best.