My opinion is that the coaching change involved both aspects you mentioned. The public image of the head coach, the recruiting decline, are a couple of reasons that I could see factoring into the decision. As well as the need to compete for and win conference titles.
We can debate until we are blue in the face where the talent level was at when Riley took over, the depth of the talent and, if you believe their was a lack of depth, how that lack of depth needed to be corrected.
I don't believe it was simply a matter of winning games and the blowout losses. I think blowout losses are becoming a little more common. Look at the results of the College football playoff in all 3 years. There have been multiple games with some pretty lopsided scores, Oregon vs Florida St, Alabama vs Mich St, Clemson vs Ohio St, Clemson vs Oklahoma. Heck look at Ohio St vs Wisconsin in the Big Ten Title game 59-0.
I also don't believe the change was necessarily made just to improve on the current W/L record immediately. Since 2011,
Mich St - Wisconsin
Nebraska - Wisconsin (s/b Ohio St)
Michigan St - Ohio St
Wisconsin - Ohio St
Iowa - Mich St
Wisconsin - Penn St
Outside of single appearances by Penn St, Iowa and Nebraska, the league has been dominated by 3 teams.
My opinion is that when Riley took over, the powers that be, SE, Riley, all of them, overestimated the level of talent and overestimated how quickly or well they could transition them to their style of play. I believe the 2015 season was an eye-opener. A more talented team would have been able to pull out more wins in those close games and a better coaching evaluation of the talent should have shown that Armstrong or the DBs and the pass rush weren't capable to running the schemes to the level needed.
I know I sound like a broken record, but it's easy to look back and say, this is what should have been done. We can all do that.
I know some are still critical of the play calling and the defense in 2016. What I saw was adjustments to better match the talent and skill sets of the players. The results showed, more close game victories, better defensive play, especially in the passing game. More play calling that utilized the strength of the QB. Had they done this in 2015, they may have won more games and built more momentum going into 2016, even more than what was gained in the bowl victory. But you can't go back.
I don't know that Mike Riley is the long term solution. I do believe that when he leaves, this program will be in a better place than when he started.