"If you don't have CPL exam passes, you can only teach LAPL. I don't know of any schools in my area that are able to teach "
Not quite true thay can also teach for the NPPL. And SEP/MEP/IMC/IR/differences training if appropriately quaulified.
"Why would a school take on an FI that could not teach PPL?"
Because there are one to two ICAO CPL holders about with 5000 hours of instruction at PPL/CPL and IR level who only hold EASA PPL and no EASA CPL TK. They might not be 'qualified' in the eyes of EASA but certainly add something that a 200 hour restricted FI can't.
I'm also know of a fair few high hour PPL holders who would also make excellent instructors and I am sure a few schools would be more than happy to work around the no ab initio PPL restriction as they also bring something to the table.