interesting you say this about an "undefined time frame" because i kind of feel like that's what the kelvin timeline (and now discovery) is. it's less specific in its depiction of the 23rd century as established by the series set in the 22nd and 24th centuries and more a general depiction of the star trek future.
i'm reminded of something rick berman said in an interview (i don't remember where) justifying why they opted to do enterprise after voyager, rather than continue into the future. he said "what do we do? make the costumes tighter?" or something to that effect. i kinda feel like the 25th century is a nonstarter. if there's a reboot, yeah just do star trek and set in "the future" and be done with it.
but no seriously, do more kelvin timeline films.