My DD is 6 and after she turned 6 we started to let her ride in the high back booster for short drives. By the time she is 7 I expect she will be ready for full time booster use.
A child's maturity is more of a telling point of when they are ready for a booster over height/weight since there are many boosters that start at 30 lbs and most kids hit that milestone long before they are ready for a booster. When a child is in a booster, they must sit in position the entire time with no wiggling or leaning or they are not safe. Most children aren't ready for this responsibility until 5+, often closer to 6 or more. DD was very wiggly in her seat until this summer. Right now, she is very reliable for 15 minute or less drives and sits well, but if we go 30+ minutes, she gets too tired and wiggly, so she's not ready for booster use full time.
If she is complaining that the harness is too tight, is it possible you are tightening too tight? You don't need to tighten as tight as you possibly can. You will know it is tight enough if you can't pinch any slack at the shoulder. Sometimes I tighten DD"s seat too tight, and she'll let me know. All I do is lift up the harness adjustor strap lever and it lets out just a smidge of tension, which is enough to let her still be tight enough, but not be uncomfortable.