That's how my children's iPads are too. Permanent downtime, with a few always allowed apps, and the rest on demand. And indeed, the most frustrating part is when my daughter needs to do some research for school. I'd have to allow each and every website she visits, so I temporarily un-downtime her phone instead...

Edited to add: for some reason, time limits never worked for my kids (they could always override them with one click). That's why I had to opt for permanent downtime.