I will just quote this post to address a few points you have raised in the thread overall. I am not a Potterite, although did see him as the best of the 2nd tier choices- after Conte, Poch, Nagelsmann and ETH. And I was a very vocal poster about wanting a DOF.
I will address the DOF first. I very much wanted a DOF to remove Levy from the footballing decisions, but that doesn't mean that I have to just accept anyone and be happy. I had reservations about Paratici from the moment he was brought and was happy with it if paired with Conte because it would be Conte driving the bus and would take away a major concern with Paratici which was managerial hires. I don't think that I then have to be quiet just because a DOF was hired or back his hire just because I wanted a DOF.
Paratici had a lot of success when working under Marotta. Once Marotta left and Paratici was on his own he hired Sarri for a year which seemed like a bad fit but they had success because of the strength of the Juve team. The next year he hired Pirlo which was a terrible hire and made no sense from say 1. They had their worst season in years as well. Meanwhile Marotta went to Inter where they won the league. I think there are plenty of reasons to be skeptical about how much of Paratici's success was due to him having Marotta above him and that he deserves a lot of suspicion when it comes to his decisions as a DOF especially managerial hires when his previous two were pretty poor.
Now we get to Fonseca vs. Potter. I think you are misunderstanding or misrepresenting the argument for Potter. It isn't that his xG is so high, it is that it is so much higher than his actual results and when you watch his team play it is explained by watching the player constantly miss chances. There is a lot of reason to think that with better players his system would still create the chances but they would get converted at a higher rate meaning the standings would line up better with the high xG. The key is that the eye test of watching them matches up to the xG and there is a clear reason for the difference in xG and standings. With Fonseca at Roma this is not the case at all. The xG lines up with the standings, what you see on the pitch also lines up with what you see in the stats. It is a team that creates and scores a lot of chances but also gives up a shit ton as well. There isn't much reason to think with different players they are better. There is no reason to think if he comes here the results would be different.
This also leads to a big difference and a major issue I have with Fonseca, and in part in comparison to Potter. Roma is team that is similar to Spurs, at least in comparison to its place in the league. Both teams are good but not great teams in the league. They have had success in the past, can compete with the top teams but are not the elite (Inter, AC, Juve vs. City, United, Chelsea). In fact Roma might be the most comparable team in Serie A to us in EPL. Brighton is not that. We have not seen Potter at a team where he has close to the resources of the teams he is going against, maybe the Swedish team did and he got that team much better results than the previous guy. Fonseca got worse results at Roma than they had in the 5-10 years before him. At Porto he took a 1st place team 3 years running and brought them down to 3rd. They returned to top of the league shortly after. Yes at Shaktar he won with a dominant team but that is one good performance with a stacked team out of 3 at biggish jobs, not good.
Yes the Roma job was tough but it seems very similar to us. Restrictions in money compared to rivals, tough ownership, lesser players. He did poorly with all that. Even taking into to consideration all the issues nobody can say he did well.
It is possible that Potter would have had similar poor results but he has yet to have them, with Fonseca we have seen what he can do with a team like Spurs and it is not impressive at all. It seems clear to me that he needs to go somewhere else to prove that he can do a good job rather than fail at his previous job and move to a similiar, or what I would say is a better, job.