Re: Turkey is a NATO country.
"it's just the only place in Europe the engines can be serviced"
I'm sure Turkey isn't the only place in Europe that has the technical capability to service the engines, especially as the front part of the VTOL system for the F-35B that the UK is buying was developed in the UK. In fact, Rolls-Royce developed an alternative engine for the F-35, but in the end the contract went to a US company.
This is purely a political move, in exactly the same way as putting the avionics refurbishment centre in North Wales was a political decision. The US needed other countries to buy the F-35 to increase the total number built, which would hopefully reduce the price down from "godawful" to merely "eye-watering", so as an inducement they farmed out lucrative repair contracts to various countries. The UK gets avionics, The Netherlands gets landing gear, Australia gets life-support etc.
This way the UK government gets happy defence contractors (always handy for the MoD worker looking for a comfy retirement gig), and safeguards a bunch of jobs somewhere that they'd like some more votes (lucky Sealand) and the RAF gets some planes. OK, maybe not the planes they wanted, but that's not really the politicians concern.