Love the thought of it. The hearthlings need more opportunities to act alive and not just be robots.
A theater should boost the morale, however, like @Fornjotr wrote, maybe something with culture as well.
The settlement could have a cultural score, that affects the net worth. Things like theater, music, poetry, storytelling, literature, art, dancing, sports (including gladiators) and festivals could contribute to the culture score. They wont be very important in the beginning, when the focus has to be on food, security and a roof over you head, but in the long run, a city without culture wouldn’t be very attractive.
Having a cultural score could give you a good, peaceful goal. It could give you more things to aim for if you play in peaceful mode or if you manage to end the fighting in normal or hard mode. Cultural activities could also take away the need for the game to throw enemies at you every day, since there can still be things happening that keeps it interesting.
So how should it work? Well one way to do it is that the heathlings do cultural activities on their spare time, either if they are idle or before they go to bed. If you want more culture you could have a setting for how much time off they should have at the end of the day. At first it could be simple things like storytelling, singing and poetry around the campfire. To upgrade it you craft instruments, masks, costumes, a stage, blank books to write in to build up a library and so on.
It could be that the most basic equipment work as the “job talismans” (or whatever they are called) so they don’t just use them temporarily but instead pick them up to “claim their hobby”. The hobby then works as a second job that they get better at over time. They might even reach a point when they can have it as a full time job.
There could be traveling entertainers that visit your settlement and perform for gold, giving your cultural score a temporary boost. Depending on the kind of entertainment the cost and boost varies.
If you have skilled cultural practitioners living in your town people can come visit to see the show, visit the library and museum, learn from the masters and things like that. There could also be challenges (quests) connected to different activities.
There is sooo many possibilities opening up if they add a system for cultural stuff. I do realize that a system like the one I suggested is advanced and would take a lot of work, so I don’t have any high hopes, but even the most basic version of cultural expression would give a whole lot more life to the hearthlings and your town.
Anyway, thanks for bringing it up. 
or playing instruments?