I'm sure the departure affected the sequels considerably, but it's mainly due to Kojima not having a lot of interest in working on "Metal Gear", is it not?
I mean, MGS3 was being developed without Kojima at the helm initially, but he was forced to step in when the team had no idea what they were doing. After that, he was forced to develop MGS4 due to pressure from fans which escalated to Death Threats.
With Peace Walker, Kojima wanted to create a game that people can pick up and play for a few minutes in short bursts. So, Big Boss was the obvious choice since he's a mercenary and it makes sense that he'd go on significantly shorter missions. Given the nature of the game, the story was clearly an afterthought, and it makes total sense the way they went about developing the game.
With MGSV, Kojima obviously was done with Metal Gear. He even said in an interview a year or two back that one of the reasons he's working on another Metal Gear instead of a new IP was that Metal Gear, given its reputation in the industry, allowed him a much bigger budget from Konami compared to creating a new IP. After that, and I'm speculating here, Kojima created the type of game he wanted to create, one entirely gameplay-driven, and made that game Metal Gear Solid V. This is probably why the game is so sparse with it's story. Not because Konami interfered with its development, but because most of the story content in the game was probably an afterthought after developing the core gameplay.
I realize this wasn't what you were trying to do, but you come across as fairly condescending at times. Like, you claim that you dislike that they gave answers to questions (sometimes to an exhaustive degree, I admit), something that most fans expected, and the reason why is because you liked your own version of the story better and others should too. I get that some freedom for imagination is nice, but there's a certain subset of people who seem to think that stories are almost always better left vague and ambiguous, and I really don't agree. I had 20 years to play the guessing game with MGS and I for one was very happy to get answers, even if some people thought they were lame. You also call a bunch of characters ruined when I almost never felt that way.
Maybe things changed after Fukushima, but to claim that he was the magic behind the series is just, again, opinion. I've found a lot of enjoyment out of every Metal Gear game I've played, it just comes in different forms.
As a side note, I see a lot of glorification of MGS2 these days. I always find it super ironic considering how many people pushed back against it after it released. The negative reaction was pretty monumental at the time. Even MGSV didn't have that kind of response and it was unfinished.
A lot of thoughts in these quotes, especially the bolded ones are some of the first thoughts I had after reading the OP. I do appreciate how much consideration DevilFox put into his explanation, but to summarize more what I think happened after Snake Eater, Kojima wanted to go in different directions after it, and people remember 1-3 most fondly. I heavily agree with people being surprised that 2 is allowed to be remembered as one of the greats, considering the reception it got; but maybe it's just the people who are talking about it most today are the ones enamored by it's high points and bold moves, and it's sandwiched between 1 and 3. As someone who loved it from the moment he played it, it's really weird to see a general turnaround about this, but time has passed, and what's supposed to be the best MG(S) has always been subjective.
I really have to wonder how much Fukushima and Murata really could have, or would have changed if they were still around. If they were still at Konami up to Kojima's departure, would we still be crediting them with some of the great stuff in 1-3, or would the consensus still be "things went to hell after Snake Eater" for some? I still look at each game as similar yet very different from each other (a strength to the series imo), and sometimes Kojima and co might've actually wanted to make an entirely different game, but chose to insert there ideas around a MGS skin; PW and V especially make me think that.
To go over OP's points,
1) As others have said, I feel the anti-American sentiment only got stronger after Snake Eater, or even anti-any established nation, generally speaking.
2) Subjective. The charm of the first 3, I think you more prefer the tone of the first three when some of the more ridiculous stuff went down. And setting aside Twin Snakes doesn't help your claim imo.
3) Given the complaints post Snake Eater female characters get about how they're depicted, I really wonder if 1-3 would be that different in judgment. The technology, as some have said, make a difference. It hasn't changed much in my eyes, but I'm willing to concede that I might be the only fan of the B&B crew and Quiet.
4) Blame 4, if it's even to be blamed. Fans wanted questions answered, and Kojima gave us many of those answers in a game set to be the end of the Solid saga. In another dimension, I still imagine a lot of people (maybe the same people), being upset if some of those questions didn't get answered. Really, I think most just didn't like the answers given.
The whole nanomachine craze and memes came from 4, and it's kind of annoying that a lot of fans think that every mysterious and unexplained thing in MGS was suddenly "nanomachines," maybe mainly because Vamp got his abilities through that. For anyone that's well-versed enough with the lore, plenty of stuff remains a mystery, and isn't explained away by "science."
And for the explaining of older characters of their younger selves, that's to be expected when you have several games set in the past. Connections are going to be made, in a Metal Gear game surprisingly.
5) We'll agree to disagree there, as I like where the lore has gone after 3, maybe as much as the first 3.
6) I've never minded a lot of the concepts he under-delivered on, even though I was really excited for some of them (more branching-hanging-shooting in 3, and 'no place to hide' in 4, even those were still present). Like the way you think of 3, I think each one came out to be a good product. Even if it was overambitious, I appreciate him trying to utilize it, even if the technology limited him.
The character switching of Raiden and Venom worked for me, and I very much appreciate them being there. I've always loved the subversion of who we're supposed to be playing in a MG game, and most of the time, I've more or less had a different or very much changed character to play.
And with the meaningful kills, I just have a different experience of that mission. As I did what I did, I recognized the names of who I had to shoot, and remember some of them from the time I fultoned them to Mother Base, and watched their stats rise, and chuckled at their awesome and ridiculous code names. Yeah, it might not be as effective as if they were more established characters with constant dialog, but I'd be expecting that. I didn't expect to care about the characters I shot because they could be just 'tools on Mother Base' to paraphrase the OP, but I did care surprisingly. Small moments of their lives flashed before my eyes as I recognized their names and how they got to the end of theirs. My description might be a little overdramatic, but just pointing out how some might experience that mission, or that aspect of TPP differently, maybe in a way that Kojima was going for (obviously whether he succeeded or not is totally subjective).
My answer of your TL;DR is I doubt that Fukushima would've made a real difference in the games you're talking about. Small differences, probably, but then again, the small things make the most difference to some. I think Kojima wanted to do different things with each game, and went for it. He was tired of it, no doubt about that, but I still love the work he put in. I'm sure Fukushima was a good team member that was lost, but I still think the games he didn't work on are as good as the ones he did.