a few people at my school do that, of course the majority don't for obvious reasons (and some of my teachers have shown (understandable) disdain towards tutoring), but some do. i know a mate of mine in a maths adv class who's told me their teacher helps them with tutoring hw at times if they don't understand it
this isn't necessarily the case. most of the time, structure of lessons is flexible, and some tutors out there really have crazy access to 500 billion resources, and i don't know what you mean by 'interactive', you get more personalised teacher attention with private tutoring than with group centres.
also another key note is that some of the smartest people in my cohort go private tutoring, so it's pretty much based on what you feel will fit you. it all just goes down to what you want in your tuition. for example, i like centres for maths because i like learning in a classroom centres and in terms of structure for lessons i want something more rigid because my primary focus is learning the content ahead of time