Logistically if Tiana were to stay at the gazebo her meet times would drastically be cut cause you can't see her in Liberty Square only to walk over by the castle and seeing her onstage in the new show
They managed it with Snow, Aurora, and Peter Pan meeting outside, I don't see why they can't manage it with Tiana.
Looking at her current meeting times:
930-1015
1030-1115
140-215
230-3
330-415
515-545
6-645
7-745
8-845
9-935
If the schedule is similar to DAWM with performances (10:35-10:55, 11:40-12, 1:10-1:30, 2:05-2:25, and 4:20-4:40)
It only interferes with 1 set. They obviously have no problem with her meeting right to the start of the next event (the set that goes right to 3, when FoF begins just down the road)
Based on past experience, her line is always pretty short in the early morning. Having 1 set missing wouldn't have a major impact on meet times for the rest of the day.
The only times I can truly see it causing problems is on the days that they have late showings. It seemed to be seasonally that shows were after dark, but those would interfere with the meets that Naveen is in as well. Considering how popular the meets with Naveen are, it seems strange that they would cut his meets at all.
It is possible that they would move Tiana inside. As I said, she has met in there before (not sure if that was before Anna and Elsa moved in though or if she was maybe just a surprise) and Naveen has met with her in there. It's also possible they will cut Naveen entirely and give him a Charming role where he appears in parades and special events only.
But if they move Tiana, then that leaves 1 open space in PFTH. Do they move Snow (who currently meets in a not-so-great location at the theater exit on main street) or Aurora (who doesn't have a meeting spot of her own anymore, and hops between Fantasyland and Main Street depending on the season). Or do they move all 3, and create a
Disneyland style PFH where it's always a surprise who will be there? But then you have the issue where Aurora currently only meets in MK, and what happens on days when Snow and Tiana are the guest princesses? WDW guests aren't as forgiving when it comes to princesses not being available as DLR guests are. The biggest problem with our PFTH is that it's only designed to have 2 meeting spaces, where DLR allows for more. They can't easily add an extra princess unless you want several of them meeting for the same photo.
And then we have the issue of Elena of Avalor joining in August. Where does a Disney Jr princess inspired by South American cultures fit in MK? She is bound to be popular in the beginning if only for her newness. Do they move her into Merida's spot (which consistently has a 40+ minute wait throughout the day) and have Merida join the PFH lineup (which would then have 6 princesses in 4 slots), or do they leave Merida, and put Elena on Main Street where Aurora used to meet (an area that would definitely need some new theming for her). Add in the fact that Elena is going to have some sort of show (based on disneyauditions.com) for at least the first few months which would impact her schedule as well.
All this to say, I don't think the logistics of having Tiana continue to meet in her glen are all that challenging, especially compared to the logistics of moving princesses to new spots while also adding a new one in the coming months.