I was a person who's first real Pokemon experience was Pearl (I came in on Gen 3, but Gen 4 was the first one where I knew what I was doing in some capacity), so I definitely have a nostalgic attachment to that. I think the basic structure can be maintained for nostaglia, but even Gen 4's fans probably won't argue that the overall region design could probably use an update (Mt. Coronet's HM saturation in particular), and there's a lot of stuff to address in the lore: How do the Creation Trio and Arceus fit into a sort of "power hierarchy" now that we have other Pokemon like the Primals, Mega Rayquaza, or the Tao Trio (and Original Dragon in Lore)? Does Arceus govern all of existence, or just our dimension (ergo are the Ultra Beasts outside his sphere)?
As for the previous third entry prospect drought, there's one very obvious aspect not touched on: Necrozma. It's speculated to be related to the Ultra Beasts, and more exploration of Ultra Space seems like an obvious means of expansion in a Gen 7 follow up, and if you look at it, it's very odd in its placement: no particular fanfare, unremarkable as is, and isn't it just kind of in the grass as opposed to a "present" encounter?
Besides that, there's both back story points they can go into as well as unexplored points, mainly with Zygarde and the Guardians. Are the Guardian Deities committed to protecting the Islands or the Islands' people? Say Lusamine's plans opened the Ultra Wormhole and the immediate means to close it would devastate the island's societies. Would the Guardians come to blows with Zygarde (who would want the hole closed ASAP to keep order) or assist it (save the islands at the cost of the people)? And at the risk of continuing to sound like fanfiction, Zygarde's just kind of there, would it have any kind of interaction with the Ultra Beasts? A completely outside factor like them would probably catch attention of a mon who already has to maintain a delicate balance with what the world already hosts.
Arceus doesn't really govern anything. It is the creator, but that's about as far as it goes. Dialga and Palkia are probably still regarded as deities in Sinnoh lore, though perhaps they'll get something special if there's remakes in the works.
I take it that the Guardian deities are all really fickle, but would probably prioritize defending their territory and facing strong challengers over the Alolan people. Tapu Koko especially is known for not necessarily coming to the people of Melemele Island's aid despite their worship, but will approach something that catches its curiosity... say, someone protecting a mysterious Pokemon that should have stayed in the freaking bag?
Either way, it would depend on if Zygarde makes itself seen as the greater threat, though the guardians probably can't quite match the complete formes' power if it can truly overwhelm Xerneas or Yveltal. Then again, the dex puts that "or" in there, meaning it's unknown if even its full power would be enough to stop both Life and
Death Destruction Pokemon at once, or even if all four guardians got their act together and worked in unison.
Now, if the Ultra Beasts did prove to be a serious threat to the balance of the world's ecosystem, then Zygarde would definitely assemble on its own to confront the threat. That's its job. But as the Ultra Beasts all apparently just really want to go back home to Ultra Space, would they actually be that big of a threat?
While for older players we would know, from a game developer perspective you want to make sure a new younger player would know. Leaving Fly, Surf, and Waterfall the way they are just makes them seem like normal TMs, hiding that they are tools to be used on the overworld for possible progression (especially if they keep in the HM roadblocks). Making them into separate HMs helps showing neweer younger players these are different from normal TMs and just in general makes it easy to find as they'll be at the bottom of the TM/HM list.
Also we need to add in the other HMs.
All that's really needed is for the NPC that hands you the move to tell you what it can be used for and add that back into the move's description. That is, if they opt to leave them as TM's and replace a couple other moves with the others, which seems unlikely considering OR/AS made Rock Smash an HM again just so you couldn't bring over something that learned it by TM in X/Y and smash your way through the Rusturf Tunnel or the rocks on the southern part of Route 111.
"The user swamps the field with a huge wave. It can also be used to cross bodies of water."
"The user charges at the opponent with the speed to climb waterfalls."
"The user flies into the sky on the first turn, and attacks on the second. It can also be used to fly to any previously visited town."
Granted, Waterfall is pretty obvious what it can do, and Alola lacks any waterfalls to think to try the move on.