I bought AOM for $3 out of curiosity for how bad it is, and to see how it influenced the direction of nu-Saints Row.
For the former, I don't think it's a bad game, just very repetitive and grindy. I just figured out that the first missions for unlocking new characters are the open world activities (kill a patrol, save a hostage, etc.) cobbled together, and this game relies far too much on dungeons that have only one aesthetic (even the likes of Dragon Age II or TES IV: Oblivion had at least three different sets). The combat sort of reminds me of a more limited version of Mass Effect Andromeda, and the overall structure is like an offline version of Marvel's Avengers (tons of different crafting materials/currencies, empty world, overreliance on the same enemy types & dungeons, and cosmetics that are mostly recolors). I'll give credit for making each character feel unique, but this is easily the weakest game of the Saints Row series.
As for the latter, I don't honestly see anything that can explain what's happening to the new game. AOM has a diverse cast of characters, but it isn't as obnoxious or as preachy as the new game seems to be. The apparent disdain for the old games isn't here as Pierce, Oleg, Gat, and Kinzie are all present (even with the change in setting, their personalities remain more or less intact). Not even the sanitization is here as the original form of Freckle Bitch's appeared in Pierce's intro cutscene. The only thing that can explain the changes might be AOM bombing so badly that it shook Volition to its core, convincing those remaining that Saints Row had to be "modernized".
Overall, even though the game's painfully mediocre, I'm not sure if it can be blamed for how the new game's shaping up.