If I may give my opinion on the matter (apologies if it seems like im attacking your wishes @Crooked-Delight , I just feel this would be the best way to bring these things up), from a business perspective... it doesn't make much sense for Sega to bring back PSO1 in any form.
I won't deny that nothing is really stopping Sega from porting any version of PSO1 on newer platforms and simply leaving it Offline... though i'd argue that not only would it be silly to have a game called Phantasy Star Online be Offline only, but in terms of Offline content well... you can play Offline through each area? Do the Offline Mode quests if you feel simply reading Rico's logs isnt enough of a story... then what? what purpose is there to grind your character to Level 200 and hunt all those rare drops if you can't play with other people... PSO1 is seriously a game that its core design was made with Multiplayer online.. removing that takes away a huge part of the game's appeal and makes the rerelease be nothing more than an afterthought.
Now lets bring servers back up right? Well aside from looking for a new host, it should be easy no? But then how will the cost of the servers be maintained? Sega can't justify having a subscription to an old game in this day and age, especially if that game is planned to be preserved in its original state and not receive any truly new content and while there is a huge demand to bring back PSO1, if this is the only people who will be playing than the game can't last long. This is one of the reasons why Online games nowadays must also maintain a casual appeal... cause if the only people playing is a small niche, then the cost of maintaining the servers may not be met in the end... after all, never forget the reason PSO Blue Burst servers went offline:
PSOBB is not making any money, in fact Phantasy Star Universe is the only reason it has been going as long as it has. Even with the lack of updates (no development, localization, or management costs), the server and bandwidth costs exceed the amount of money generated by paying subscribers.
^ From the old Sega forums
Now a remaster would be nice but what I think PSO1 needs in order to be brought back to the full extent most people want it is a full on remake. Rather than simply take the same game and give it better graphics, PSO1 needs to be remade and adjust things that haven't aged well as well as provide an experience that can get not just retro fans but also new fans. In my own personal opinion he is what a PSO1 remake should do:
- Use the more 'evolved' PSO1 gameplay used in Phantasy Star Zero as a basis complete with lock on and dodging.

- Bring back unfinished features such as the missing HUmarl and HUnewm.

- Tell its story in a way that makes it feel less like an afterthought.
- Introduce quality of life features introduced in newer games; being able to feed your mag anything and seeing what stats will rise beforehand, having a visual display for the amount of Mats you've used, a Common Bank, etc.
- Find a balance between preserving aspects of the original and having truly new content that will keep players coming back (content releases is what keeps players coming back in an Online game... simply having the same game be stuck in a 'time capsule' isn't going to get people to keep playing except for the most dedicated of fans).
- Elements of online games that were just gaining traction in the past updated and streamlined to its modern equivalent.
Of course, I can already imagine people who are opposed to this and instead demand the original game as it is to be brought back... to which there is one way that is indeed feasible.

Assuming that SEGA still has the original source code to PSO and can make a new PC port (or still have the source code to PSO Blue Burst which is already on PC but is Online-only) and rework its netcode to rely on Steamworks' free to use Peer to Peer servers. While this means the netcode will take a minor dive (as the game, including lobbies, become FULL peer to peer) it does mean that there's no cost to keep the servers up and Sega can pretty much leave an untouched version of PSO up on Steam. No demand for new content, no need to appeal to casuals to get that extra money, just the same game exactly as it was originally.
And hey... maybe I could be wrong, if Xbox Live work in a similar fashion to Steam's servers then maybe this is possible on Xbox One and Windows 10 ...
But hey, this is all my opinion... what do we all think in here?