Should health tourism be allowed?

Hi guys so quite a controversial topic of discussion. However, it is good to have this debate. Quite a few people travel to the UK to receive free health treatment. Even if charged for the treatment the costs are so astronomical that realistically this is never recouped. So the question is, should people be allowed to travel to the UK for free health treatment having not paid any tax in the UK to contribute for the service?

Theoretically they are contributing elsewhere such as paying for food, room, travel, etc. while in the country which does contribute to the economy. I don't know how much that would even things out there. Also theoretically they are creating (non-quantifiable) goodwill for their country which could have positive effects outside of the economy (such as in international dealings and diplomacy or non-medical tourism). Further still there is the possibility that they entice a potentially productive and contributing person to stay in the country who would then add value to the system as a whole.

There is also the humanitarian argument that if it's possibly for them to treat someone, to provide aid, they should.

To me, if you are going to have socialized healthcare, only citizens should receive the healthcare. That is the purpose, right? Everyone contributes a little bit to the greater good? If you are a medical tourist, you haven't contributed. Lets assume (a huge assumption) that the tourist contributes more or the same as the cost of the operation (difficult to calculate, but for sake of argument) by staying in a hotel room, paying sales tax, etc. Well, now the system is helping one person and not helping another citizen. Why should the person who is 1) not a citizen and 2) hasn't contributed be prioritized over a contributing citizen?