I want a new manager next season, so it's not really a defense of him from me.
Also, that analogy is terrible. The CEO of a company is literally there to make decisions that affect the whole business (or delegate accordingly). They live and die by that, and Manchester United quite literally have a CEO above Ten Hag who should have stepped in and stopped his hiring if this control was one of the terms. In a business context, it'd be like hiring a manager for your IT department on the basis of them having significant control of your marketing department. It's simply silly to agree to such terms.
I agree that there are concerns regardless of who is to blame for recruitment failings. Antony was his player, he'd worked with him extensively, and he's got feck all out of him. That's a fair criticism, but it's also one we don't actually see much of, because instead it's just "£400 million spent", "16 signings". Similarly, prioritising Mount is a confusing move, as was the sustained pursuit of Amrabat given his clear unsuitability to Ten Hag's tactical preferences.
Yes, I understood your point last time. The the third bullet point isn't true though. At least not the extent (people believe) Ten Hag has control. Literally the only control we know Ten Hag has is a veto over suggested targets. By default, this suggests that others have (some) responsibility to identify and suggest potential transfer targets, and then he reviews these and gives his input. It's possible that he also suggests his own targets, but if they've not been scouted extensively or the scout reports don't show them to be suitable, we shouldn't be pursuing them just because he said he likes them.
To flog a dead horse, we had scouted Antony. We reportedly valued him at around £25-30 million, which would have placed him firmly in the "squad player/rotation option" part of the squad. We reportedly asked Ajax about him and walked away when they asked for £50 million. We then failed to sign an alternative, panicked after losing our first two games and ended up paying three times what we'd valued him at. The majority of the blame for that has to be on the club and the recruitment team, regardless of how much Ten Hag liked him.
To flog another dead horse, Klopp wanted Brandt (and apparently two or three other players) ahead of Salah. He was overruled because Liverpool had done their homework and Salah was the stand out candidate for the position. Managers, in modern football, do not dictate transfer policy to the degree that it is made out that Ten Hag does. Some will take more of a backseat than others, but it's simply not true that Pep, Klopp, Arteta or anyone else is coming into a club, and going "scrap your scout reports, I want these players," which is what is repeated about Ten Hag again and again.
Emery had no control. There's a large middle ground between the club signing players you don't want, for huge fees, and being able to ignore all of the work the recruitment team has done in favour of "at all costs" pursuit of your own targets.
This is why this debate rages on endlessly, because one side (not you, specifically) inevitably ends up making out that signing two back-up goalkeepers and Wout Weghorst on loan was somehow part of Ten Hag's master plan for the squad. It's also how we end up with straw man comments like "Ten Hag signed Martinez and Hojlund, but Murtough signed Antony and Amrabat".
You can criticise Ten Hag's ability to lead recruitment strategy, but it's not really a concern when we should primarily be concerned with his ability to manage the team. As I said above to RedRover, Antony's lack of output is a massive concern, and on a related note, prioritising a left-footed right-winger as a key element of his tactical system, only to end up playing a right-footer there, who has been far more effective, is another actual criticism to be made. Ten Hag should be able to brief the scouting department on what he needs for his system to work, and Antony and the Varane at left centre-back thing are two large examples of him seemingly not knowing what he needs, which is a massive indictment on his managerial capabilities.
To use yesterday's favourite word, this endless harping on about how much control he has of transfers (and how much leeway he can be given because of the injuries) obfuscates any real discussion of the more pertinent issues. It's tiring, and when it's (supposed) United fans endlessly bringing up the same, weak points over and over, it makes me think that we're just going to be here again with the next manager as soon as we have a couple of disappointing results.
ETH has had his share of horrible losses as well.