His problem in my opinion (as always with Real Madrid) is their football is a souped up, glorified version of Man United's boring counter attack from the 90s. Guys like Bellingham, Vinicius, Guler, Valverde, Mbappe etc are pretty poor in tight spaces really, and not great on the half turn (relatively speaking) so they'll continue to get outplayed and dominated by teams with more cohesive systems, positioning, and better technical midfielders - like they were last season against Barca and were the other night - to noone's surprise in the latter case given how good PSG were this season.
The problem Alonso has is he seems to wanna play more like a Klopp or Pep hybrid - lots of high pressing, turns and feints in small spaces, wriggling free and opening up space with ability and movement and turns in tight areas. But can this team do that? In flashes maybe, but not consistently throughout the 90 or throughout numerous matches. Hence, Alonso seems far more like a Barca type of coach (I know he played for Real) than he is Real.
Trent Alexander Arnold is another example - at Leverkusen Alonso had Frimpong who is a runner, works hard, can dribble. Alexander Arnold is more of a crosser and passer from deep who struggles defensively. He doesn't seem the type of up and down the flank full-back or wing-back that Alonso would like.
Ancelotti was never a particularly great tactician. His game was built on being defensive and allowing the output difference makers to shine in moments. Jose and Zidane the same. Alonso seems a bit more complex than that, but I think these players he has there are not the sort of players that suit him to get the best out of his coaching ability.
Honestly, if they weren't such a massive club, he wasn't Spanish, and he hadn't played for them, would we have said he is a good fit for them? I don't think we would.
Honestly, it feels like they have no plan and are just making it up as they go along - signing anyone considered a good player with a big profile. They can still win trophies due to their moments and highlights but they won't dominate teams like PSG (and Barca) do.