It's no surprise this sort of thing would pop up. It's not unlike the problems that arise due to things like car sharing and airbnb, when insurance companies and landlords get involved.
Insurance companies are probably willing to let it slide if you let someone else who's insured drive your car, and landlords generally allow you to have guests. But lending your car to complete strangers, for money, and letting complete strangers stay at your apartment, essentially short-term sublets, are not really what they are prepared to tolerate, at least not without altering the terms and rates they charge for coverage or rent.
Insurance companies are probably willing to let it slide if you let someone else who's insured drive your car
Not just probably: I called my insurance to put someone on my insurance, and the customer service rep grilled me about how often they would use it and for what purpose ("Are they using it to commute to work?"), and then strongly recommended I not buy any additional coverage, stating that my existing coverage covered them as well, no problem.
That's not the case. The difference in driving laws (right vs left lane) makes it fairly difficult to move cars between GB and mainland Europe, because cars have to be physically modified.
Insurance companies are just out to make as much money as possible; in Europe their life is hard because they don't enjoy the ridiculous margins from crazy markets like US healthcare, they have to obey stricter regulation, and suffer from heavy rates of fraud in many countries.
Yes, but this is not comparable to cars being "spirited off" across the continent, which don't need to be split up or modified: I can move a car from Prague to Paris and get full whack for it. This is not the case for the UK market, which enjoys a little bit of a barrier compared to the rest of the EU. Proof of this is that the secondhand market is still very much alive, because car prices are higher than elsewhere, since there is less pressure to align to cross-European prices. That is not the case in, say, France or Italy.