I hold basically nothing sacred when it comes to the series, I think Shenmue is at it's best when it's using any tool at its disposal to tell the story as effectively as possible. I also think that the best way to "modernize" Shenmue is to start again from the beginning, especially after S3 maintained the status quo. I think a huge gameplay shift at this point would just serve to piss off existing fans and be too little too late to attract new ones (though I know this won't happen). With that being said:
- Fix the stilted, robotic dialogue. Remove useless button presses, like pressing A to simply continue the conversation, dialogue skip is a big one, have more natural voice performances (I play in Japanese and I do not consider the bad English dub an asset), remove the ability to speak to any NPC (this is probably the single biggest budget-reducer they could do), instead have NPCs react contextually to Ryo (children can just passively say "hi mister" to Ryo as he walks by them). The more characters sound like humans, like Ren and Ryo in S2, the better Shenmue is imo and the less meme-able it is.
- Figure out how to handle money: if Ryo is supposed to be strapped for cash, then make an artificial limit on how much he can carry. If I started S3 with my S2 money, I wouldn't have had to grind (but the currency is different) so it's hard to know what's intentional, I personally don't think it adds much outside of Ryo needing money for Hong Kong and having his bag stolen so I lean toward just letting the player amass however much money they want and have that continue between games.
- Anything that halts progress, has an instant fail state, or just plain doesn't contribute to the experience in a meaningful way needs to be gone or modified (ie: the stealth is much improved in S2 over S1). Shenmue has this reputation for being the most relaxed, slow-paced game ever and yet it has these crazy intense instant-fail arcade sequences.
- Better integrate combat into the game. S3 does a great job of allowing you to train at dojos (though I'm pretty sure they're not called dojos in China) and this should be a bigger part of the entire series, but I wish the system was more robust or at least required some strategy/tactics.
- Make Ryo's journal an essential part of the experience, allow him to select the objective that he'll talk to NPCs about and make "filling it out" more of a progress indicator.
- Figure out how time should work: is everything governed by a schedule or not? It seems to me there's potential for interesting interactions if Ryo has to balance his detective work with his day to day life, so rather than force the player to interact with Shenhua, make that a choice.
- Make interactions faster. It can still be a slow-paced game but there's no need for environmental interaction to feel so stiff. And reduce the amount of useless interactions, there don't need to be 500 identical drawers to open with nothing in them, and remove cutscenes associated with interactions. I don't need to see a close up of Ryo's face telling himself no one is home every time I knock on a door.
- Shenmue takes place in the 1980s: the fashion, locations, technology and in-world music should be more evocative of that era. S1 and 2 were great in this regard given their limitations and it honestly feels like the S3 artists forgot when it took place. And, I can't believe I have to say this, but it also takes place in China, so no Japanese shrine girls. Also also, this is extremely petty but I prefer real world locations (apart from Bailu Village), and I didn't much care for Niaowu being fictional. For a series so steeped in a specific culture and time I think it's very important to get this kind of thing right.
- Completely redesign the UI to fit with the more minimalist, modern UIs that players are used to.
- There are enough buttons on a controller to not have the face buttons pulling double duty.