I am only going to repeat what I got told OP and lord knows, I found it SO stressful deciding on my dd’s braces!
First of all my dd has been on wait list for braces since age 8. Waiting for mouth to grow, then covid, then waiting for last baby tooth to fall out. Finally told ok can start treatment. Now 14 and got her braces 6 months ago. Overbite of 1.1cm (yes, massive). She had an accident and broke two teeth which complicates things (one tooth is dead).
Anyway: I consulted three private orthodontists and an NHS dentist. The distilled advice was “we avoid removing healthy teeth any more for orthodontic work because it causes problems later in life. However there is an ideal time to widen the mouth to allow all the teeth to fit in, so we need to get on with it - why did you wait so long we prefer do this during the main growth phase which usually ends by age 15 but we can do it later, it will just be a lot slower. We will do everything to avoid removing teeth, braces have moved on a lot since the 90s when you had teeth removed. Nowadays removing teeth is a last resort and if we have to remove teeth we do so in pairs to avoid the mouth ending up asymmetric - your smile can end up slightly off centre if only one tooth is removed.”
Of the four dentists, only one thought removing teeth was a possibility and even he said he’d rather try braces first to see if he could reconfigure the palate.
I was told dd could get NHS braces or private. Payment plan for private was offered. Same dentist, different technologies and prices. I have paid for invisalign private braces - VERY expensive. But within weeks seeing a difference and now 6 months in the overbite is already almost gone and we still have 18 months of treatment left. Dentist told us outcome will be “aesthetically perfect” and dd is pleased although it’s not an easy treatment (blocks to retrain her bite can make it difficult to pronounce words.)
I discovered it’s not a straightforward “single solution” treatment - if you break a leg, someone fixes it with a cast and a bit of physio. No debate. But with teeth there are different approaches and every single dentist we saw said something slightly different. Baffling to be honest.