It would be simply a creative choice by PIC's producers if they went that route, because otherwise CBS had the final say in the design of the Enterprise-F and then made it licensable for merchandising. The fact that it is a STO design wouldn't be the issue if PIC went with something different.
Anyway, we're all assuming that the new ship is going to be the Enterprise-F, but do we know that for certain? Aside from that it would make the Enterprise-F the third such ship with the name within four decades (yikes), it could be that the Enterprise-E is still in service and this is a new vessel with a different name. It is possible that the TNG gang moved on from the Enterprise at some point after Nemesis, and would fit the general sense driven repeatedly home throughout all of Season 1 that things aren't like they were during TNG.
An Enterprise could still make one or more appearances in Season 3 of PIC, but it doesn't necessarily have to be this new ship. If anything, it would drive home that even with most of Picard's old command crew back together, this isn't TNG Season 8...