Honestly? I think Hayter is Snake, much like Kurt Russel will always be Snake.
But Kiefer actually can act (... when he is not struggling with his demons and tackling Christmas trees). And basically from MGS2 on, the decision was made that MGS should have pathos that is not "so is this intentionally funny?" a la "Can love bloom on the battlefield?".
MGS2 sort of got away with it because Quinton Flynn is actually a pretty talented VA but... everyone hated Raiden because he was "the player" rather than "Snake". Same gag as Otacon but people sort of realized it this time.
But MGS3? I am not going to claim that the issue was that Hayter "couldn't do the voice" or whatever. The issue is that he just isn't the kind of actor who can carry those scenes. And that is why we mostly had EVA (unknown, but likely a "real" VA/actress) and The Boss (Pearl Krabs) carrying the story with a lot of the more emotional scenes involving Naked Snake silent and in agony.
And MGS4 was the worst of all worlds. Between having the player mockery character fuck the fanservice version of Bastilla for no apparent reason and actually putting a lot of the pathos on Hayter and Meryl (Debi Mae West has a fairly limited range) and some random kid... yeah.
Which gets to MGS5. When Kiefer speaks, he knocks it out of the park. His career is largely built around taking REALLY mediocre scripts and somehow making us care about some obnoxious bully or a psychopath running around with a car battery. But apparently "lessons were learned" from MGS4 so it was mostly awkward silence while Kaz or Ocelot did the talking and... yeah.
Still, if you can get past the trademark Kojima misogyny, MGS5's gameplay is miles beyond every other Metal Gear short of Rising. It does have the problem of trying to shoehorn in a progression/unlock system while giving you a silenced (later infinite silenced) tranq gun (and tranq sniper rifle) in the first three hours of actual gameplay, but that actually works with the general horrible pacing and lack of plot (and spoilers built in to the intro cutscene of every level...).
Although, if you have the option, play it on PC and fiddle around with one of the bigger mods. Doing more missions as OSP (start with no gear) and tweaking the progression so that the top tier stuff isn't balanced around multiplayer goes a long way.
Still. 4 with a more talented VA (and a lot less fanservice) would have been so amazing.
Much like Escape from LA was shit compared to Escape from NY, the MGS series has gotten progressively more and more hindered by being built around a "... how did you not get sued?" reference to Kurt Russel in the 80s joke. Like I mentioned elsewhere, I really wish MGS had become an ensemble piece (and MGS2 was trying for that before the backlash). Rising being a character action game as Raiden is AMAZING. Imagine an IOI led Hitman-style game where you play as Meryl or Johnny infiltrating an enemy base. Or an Arkane led game where you play as The Cobra Unit with all their magic powers. And not having to keep going back to such a one dimensional character as the core of the series.
Also, just to make it clear. I am not shitting on Hayter. Bruce Campbell is one of my favorite actors (also was in Escape from LA...). He can do very short bursts of pathos but it was clear that Burn Notice was struggling when they had to rely on Bruce/Sam because Michael/Jeffrey was still learning how to act and it would have been INSANE to let one of the better tv actresses of all time (Sharon Gless) do anything other than play a one dimensional character. Not every actor is Lead material and that is fine. Because you need a lot more top tier supporting actors/actresses than you do "good" Leads.