The critique is justified. There is a difference between moving up when you see pressing is making a difference and the opponent scrambles to play out, and moving up when the press is not working and opponent finds open players with ease. Which is what we're doing. Even Pep Barcelona played with a high line often.
When pressing works well, you move up and get more aggressive with the high line. When you see pressing is not functioning effectively, and the opponent has free men able to receive, you keep more conservative positions. Flick doesn't have this filter, he will put the high line, and assume the pressing has to work all the time. His approach is press like a beast, or suffer the consequences. With a short squad, and exhausting season, with injuries to your best players at the wrong time, you have to add more to your gameplan than just press, press, press all the time.
The combination of high line and inefficient, weak, or hazardous pressing is the real problem. Not the high line per se. It was always like this. We can look at many Barcelona teams in the past that at moments played with defenders at halfway line, but it was far more controlled than Flick's erratic version.
You always move up when pressing works, to keep the team compact. No serious team combines aggressive pressing and keeps a low block back four because that would mean you have 80m between the first and last lines. Which is a big no-no.
Flick has moments where he plays with a mix of approaches and this is when he is at his best. For example the Bayern 4-1 match was 2 matches in one. First half an hour it was a blood bath with similar approach from both sides (not unlike PSG vs Bayern), but after 30 mins or so, we started to manage and control the match better and kill off this end to end roller coaster pace. He has moments where he is flexible, but these are too rare. This should be his main approach, not something we see every once in a while.
Flick would improve if he would embrace the idea that we are FC Barcelona, a Spanish side. And Spain are Euro winners because of a higher ability to control the tempo of games compared to France, Germany, England. Tap into that more. To make the midfield thin in numbers and over-load the attack is to give away this advantage more than we'd prefer.