TTS has been getting lambasted for almost 2 decades now. It was "well-received" because it served its purpose as a remake. It was not well-received because Kojima shoved Ryuhei Kitamura down everyone's throat (I love Kitamura's work, but he's a bad fit for MGS), the re-recordings are mostly fine, it's script changes that really soften the experience. Kojima had little input into MGS1's localization and Jeremy Blaustein delivered a punchier and natural script, but, by TTS' development Hideo had creative control over all aspects of the product. He "sanitized" it to his liking and as a result the script read and ~sounded~ closer to MGS2 than MGS1.
All that said, I think the overall product works. You might not like Hayter's rendition in TTS, but it's more to do with the fact that Hayter in MGS1 was trying to establish that voice. It's like John Dimaggio and Bender. If you compare Bender in the first season of Futurama to Bender in later seasons, they're similar... but you can definitely tell Dimaggio "got" what he wanted Bender to sound like later on.
The only major complaint I have with TTS is the fact that they should've never recast Gray Fox, and if they had to... Rob Paulsen does not work at all. He sounds ~different~ but he also brings nothing to the role except literally sounding "different", such a waste of a great voice actor.