I agree that the slow pace is interesting, and going for a more down-to-earth style of setting and feel. However, I feel there's two contradictory elements to this that work against the idea realizing itself: First is the dynamic time working the way it does, it ultimately just makes it impossible to relax and let yourself sink into the world because you're in a constant hurry. Second is that it both transitions to martial arts epic abruptly, quickly, and clumsily, which is made worse when these two contradictory styles start to overlap (the harbor and Mad Angels bit is to me easily the low point of the game). These both I feel are compounded by the fact the world engages you in a very passive manner, since as I mentioned I never really got a sense of Ryo's other two friends were anything more than just throwaway NPCs. I suppose this overall problem with Shenmue in this regard is that I feel it doesn't fully realize its idea of slower pace and the mundane and indeed sweetly nostalgic small town settig.
The other major problem (I'm entirely going to disregard that its controls have aged very poorly, since that's only really a grating thing when you start and when you fight Gollum for such a long time; similarly I'm not going to how the lack of stuff to do in the world against the game since it did everything it could with what was available at the time) is really just that you end up with a lot of repetition. I suppose a good comparison of this is how Shenmue handles the forklift minigames, and how Yakuza handles for example the hostess club minigame. The forklift minigames take a relatively huge amount of time, and the race is always the same. There's a bit of fun in figuring out how you can handle the crates most efficiently. But overall it just takes too long. By contrast, the hostess club minigame is fast as hell, with a sense of working towards something, and very importantly it comes with its own side story and characters.
If anything, I wish Shenmue had been more slow. I would have liked to see Ryo actually go to school before dropping out, I'd have liked to have at least some neighbourhood cop (since it just comes off as strange how the only time cops are even mentioned is if you try and call them at the start and Ryo's all like "fuck da poleez, revenge time nao"). Get to the Phoenix Mirror, Gollum, and Master Chen much much later, not before Ryo's figured out Lan Di's going to Hong Kong. Also, design of the game could have either been focused and given more action or puzzles so it's not point A -> point B most of the time, or given a more open-ended structure (I'd prefer the former) where you have lots of ways to get to Hong Kong. Focus is also something it could have used (ie, cut the harbor, focus on Dobuita and Sakuragaoka), since while indeed there's a lot of thought put into the characters there's ultimately very little many of them have to do for you or time to visit them. This is another thing I feel Yakuza improves on, since while it doesn't populate a small community it does focus and create very memorable characters and situations, while also adding a whole lot of big heart and compassion to things; Shenmue I feel is too passive with its NPCs, and Ryo is not quite the local superhero that Kiryu is. Of course, this is kind of a key difference between the two games, where Ryo is despite blatant shounen protagonism's a fairly rooted part of his world. Kiryu on the other hand is larger than life and very much a Hero that is unshaken and insurmountable who is here to save the day of anyone he encounters because that's his mancode (although I'd say a thing that separates Kiryu and his co-protags in Yakuza from the usual video game fare is the level of empathy and compassion they engage the world with, they aren't brooding angry edgelord sorts but confident manly men with hearts even bigger than their fighting prowess). Though this is also often used for contrast humour in all the situations the baddest dude in Japan ends up in and deals with sincerely and earnestly.