No, why would they? But you'd not owe a penny to the UK. The idea is to remove the attraction of tax havens.
The trouble is you pay tax in different ways in different countries. I don’t know about Monaco, but Dubai for example is 0 income tax, which sounds great.
However you have to pay for medical insurance and schooling, there is some form of council tax and it’s just under £1k a year for a visa. Everything you do- ID cards, driving license, car registration etc there are inflated government fees to pay. There’s a low VAT of 5%, but eat out and you pay an extra 10% service and 7% municipality fee, and that’s on top of import tax of between 5 and 50%- and almost everything is imported. Boat loads on sun tan lotion too! It does work out better here, and more advantageous the more you’re earning, so especially in the context of f1 drivers, but it’s not just 0 tax.
I also don’t use any services in the UK and don’t particularly plan on ever moving back. The idea that I’d financially tied for the whole of my life to a country that I don’t have much to do with seems mad to me.