Exactly. Yes, playing a high line while being forced to play slow CBs when the fast ones are injured would be suicidal. But if you value control over matches, the smart thing would be to keep possession, but deeper. Try to bait the opposition's pressing, before launching fast attacks, but stay in control, keep possession, stay true to your basic philosophy.
If you instead sit deep with your defence, position your attackers quite high and ignore the midfield, then you simply don't value control and possession but want to play the transition style. Would that look less broken with a higher defence? Yes. But it's still a deliberate decision to "break" the team instead retreating the attackers a bit as well. So if that's what EtH focuses on now, no one should expect him to build a possession side at United soon.