There's no issue with him looking to implement a more direct & transition focused style than he did at Ajax. A lot of excellent sides fall into the category of being more direct and transition-focused than Ajax. Klopp's PL/CL winning Liverpool team were famously more direct and transition-based than their rivals City, but it wasn't seen as some concession to not playing "a modern style of football". Fast, direct, attacking football focused on regaining possession in dangerous areas through aggressive pressing would be great.
Plus, these stylistic differences are relative. A league winning side who focus on possession are still going to be better in transition than nearly everyone else in the league, and a league winning side who are more direct and transition based are still going to be better in possession than nearly everyone else in the league. Because that's what being good enough to win titles entails.
The real problem is that whatever vision ETH had in mind for United, what he's built up to this point is a side that are quite bad at excecuting it. If we were playing a high quality version of that more direct style ETH envisioned then there'd be few complaints, but instead we're bad at being even that. And ultimately it doesn't matter what your stylistic preferences are if you can't get the team to be good at doing it.