I am always surprised when people dont realise that state school teachers and independent school teachers are the same people, from the same training courses, with the same qualifications, and who work in different schools at different stages of their career.
Most teachers in my school have masters degrees . I do. many also have PhDs
The only difference is that they will all have teaching qualifications too.
You dont need a teaching qualification to be employed as a teacher in an independent school. Some of the most prestigious schools in the country go round local unis recruiting undergrads as junior teachers, then employing them full time after they graduate.
These particular teachers will spend their entire career in the independent sector, as they will not be qualified for the state sector.
But those of us who are qualified teachers move between the two sectors according to stage of career, family commitments, personal preference etc.
As a qualified but inexperienced young teacher I worked in a private schools that required boarding duties. That has never been an option while raising a family, but I would consider it again now
There are disadvantages to private schools, behaviour can be very poor, bullying of staff both by students and parents. Health and safety and supervision is nowhere near as tight, staff facilities can be very poor indeed, and hours can include many compulsory Saturdays
And, contrary to what you might think, some private schools are worse funded than state schools. Just because they are funded differently does not automatically mean they are funded better. The school I was in, for example, had no cleaning staff, instead they offered a free room to any couple who would clean the school once a day, hours they could choose themselves. Sometimes this worked well, sometimes the room stayed empty and the school uncleaned.
The biggest issue I have found in a private school is no supply staff ever, as they are not budgeted for, leading to classes being amalgamated beyond the point of safety, and reasonable accommodation. Once, a teacher alone with 3 classes had to deal with a serious asthma attack, and the 3 classes were left unsupervised crammed together in a tiny room. Nothing bad happened, but it could have
Anyway, this has become a long post - my main point is that there really are not two pools of staff, one state one private. There are two pools of staff, one qualified, one unqualifed, and the unqualified teachers are mostly in private schools, and the qualified teachers move around between both