I've also leaned towards there's no Enterprise in the 32nd Century. I don't think there's been an Enterprise post-Burn at all. I think the Enterprise symbolizes what Starfleet used to be and is trying to get back to. I think a new Enterprise would symbolize that Starfleet is completely back on its feet. I don't think they'll get there before the end of Discovery.
I'm curious. Why would the Enterprise signify that?
The Voyager crew would (if anything) deserve that honor because Janeway was adamant about keeping up with UFP principles and ideals.
Yes, as the years went on, things were slightly 'modified' to fit better with the circumstances, but they still behaved largely in accordance with those principles and ideals while in an unexplored part of space with no backup.
Also, its entirely possible the Enterprise simply isn't active in the 31st century.
It may have blown up in the Burn, or SF may have just given the ship a rest for a while (a 100 year break perhaps because they had limited resources and no ability to make new ships - although I take issues with that because with replicators and programmable matter, not being able to make new ships without an actual drydock seems... ridiculous, because that whole SF HQ could have acted as a shipyard given the tech there).