having bounced around a few community bands over a number of years, I'd say that yeah, the tenor parts are worse. It wasn't so bad in a band that was very sparse in the middle voices because I had meaningful space to fill, but in other band more well attended and organized band, I was almost superfluous.
I'm playing bari last few years and I do prefer it. I'm not a great player so for me, its more about going out and doing something that keeps my lips warm. That said, I sit near two stronger players, one who plays bassoon and the other bass clarinet and bassoon. Sitting there I can easily say in comparison that the Bari is the most unnecessary of the three. All things equal I'd take the bass clarinet first and then the bassoon before making sure the Bari Sax seat was filled.
I feel most useful in jazzy 20th century hit medleys, and hold my own in marches.
The absolute worst thing about it is the seating positions. I understand why you want the low instruments in the middle, but its a fetching pain maneuvering around a messy band room with #@&@#$ Baritone Saxophone tied around your $%$&@! neck while carrying your music in your other hand. I have to get their early just to have any resemblance of ease getting my position set up.
And that's the problem with large instruments. You can't just sit down, slip into your seat, take the instrument out and put it together while its case rests on your lap. With a bari sax you gotta' get "set up". Small instruments get to sit on the peripheral parts of the group and slip their case under or besides their chair. I gotta' store mine elsewhere in the room. I have to often take multiple trips across the band room to get ready, and often multiple trips to get stuff in my car when going to remote concerts.
What makes it worse is that most other players who sit on the sides have little respect for your troubles. One alto sax player in my group often pretends she doesn't notice me when I try to slip past her trying to get to my seat on a crowded floor. "I'm here, I'm comfortable, your plight is your problem." is the vibe I get.
I can't just get there early, I have got to get their first by about ten minutes so I have time to get my stand and chair set, get the music on it, take the instrument out of the case, hook up the harness, grab the mouthpiece lig and reed, stow the case...somewhere and get it all together by the time the tenor and altos show up or I'm going to be dancing around a shitshow of bodies, cases, and other obstacles in an overweight, chicken-legged German body while waving around a ten pound instrument made of butter-soft brass. My equipment is very humble: a troublesome, century old Buescher and a Mexiconn I have just brought into service over the covid break. I've always wanted a more modern bari, but for the life of me don't think i'd be too excited about subjecting a nice horn to this environment.
I like playing bari. The sound is good, the parts fit what I need right now and I enjoy the group. If I ever quit the bari, and I'm sure that day is coming, it will be because of all the logistical bs, not the repertoire.