For many years I had valid licences from France, Quebec, Florida (which is the one state that issues "Florida Only" licences to snowbirds from other states and provinces). I had a UK diplomatic licence: they issue the old red books and are valid only for three years, renewable only if you still are on the diplomatic list.
Eventually I realised my French licence (I got it free as a diplomat) was no longer valid because of my age despite having no expiration date, and not transferable to the UK because I never took a test. So I took a UK test and gave the French and Florida licences to my Swiss canton, which sent the (invalid anyway) French one back to Paris (irony: my address on it was 2, Av. Gabriel) and gave me back the FL one with the sticker.
But I can't ever drive my UK car to Switzerland: my UK-resident daughter would have to do all the driving. I rent from the CH side of GVA Airport when I need a car. i thought of getting a folding eBike, may still do so. As I am registered at the Contrôle des Habitants as Swiss domiciled at the flat I own, I can only drive with a Swiss licence and foreign commercial lorries and international buses (I actually had a NYS Class 2 bus driver licence once) aside, so long as they are taxed in CH, a Swiss car with a Swiss licence in Switzerland; and I can only drive a UK car in the UK with the UK licence it is a conundrum for which the old advice that "more people got hanged for volunteering information than for any other reason" holds true.
Point to remember: never to let any EU customs or peace officer get a glance at my UK licence. Or has Brexit changed that already and are we on to bilateral agreements? (Which don't always work: lots of US states don't recognise Puerto Rican licences!)
I turned in my QC licence after 60 years simply because I no longer go to Canada. And it costs C$100 a year. Also closed my PO Box in the border town where I've had it since 1970. I remember taking the QC road test back in the day. First they rejected my parental consent form (age of majority was 21 then, and my mom had signed it, not my dad). When that was fixed the testing guy spent the whole time playing with the air conditioner of my NYS registered car. He'd never seen one before.
PS: Passed the UK test on the third try.
PPS: I have USAA UK insurance which lists my daughter as a driver and is valid for any driver using my car with consent, and for either of us driving anyone else's car in Europe, USA or Canada. Doubt if I will buy a Swiss car anytime soon. Even in the UK the only driving I do is to take my grandson to his French school in the morning. When I do rent a car in GVA I rent online cheaply and use my Chase Sapphire Reserve card which gives free primary collision cover with no deductible. (I used to use Amex but they were secondary, so they'd just pay the USAA deductible; only had one claim when car was dented by a hit-and-run in a museum parking lot.)
PPPS: OP's other gnarly problem is insurance. You have to tell your insurer all the facts, even those never asked, or the policy is voidable. I've seen policy claims denied by the AA's insurer because a car was routinely parked "too far away from the designated home address". Around the corner I think it was.