In my experience, the main 'national chains' of these are a 'one stop shop' for a little bit each of three things that are all better taught separately, but where the single venue and single time are convenient for many who do this more 'for fun' than anything else.
Potentially, they can also act as 'gateways' to the more serious 'single' providers - so if you like the dance side, you can join a good / serious local dance school to do ballet + modern theatre exams. Or if you like the drama side, you can join the local theatre's youth company. Or if singing is your thing, you can find a solo teacher or a good local youth or schools choir or even church choir if you want to learn to sing better.
Also, despite being a national name, each franchise will differ in the genuine expertise of their staff and their ability both to train their pupils and signpost them to next steps.
So if you are a parent or child looking to have fun, be out of the house for a few hours each weekend, gain confidence and get to be on stage, they're fine (though as said before, the franchises vary). If a child is genuinely serious about improving as a dancer, singer or actor, then with a little searching, the highest quality training in each is probably found elsewhere.