There's not much I can add which hasn't already been said but I wanted to add my voice to the notes of caution coming from the point of view of an adult child left behind in this situation.
I was 21 when my parents left to live on a fairly remote Greek island. I was genuinely delighted for them, and in many ways still am - everyone should be able to live their dream, no matter what your age BUT living your dream comes with strings attached - in this case the need to plan very very carefully for all eventualities.
At 21 years old (my parents were mid-50s) I begged my parents to look into the Greek healthcare system and to consider what would happen if one or both of them became seriously unwell. I also impressed on them the benefit of keeping a base in the UK but they laughed all of this off, saying I was being morbid and they just wanted to set off for a life of sunshine and happiness. Beyond that, whatever would be would be...
On the plus side, I do think they became healthier and lived a better retirement than they would have done here but my dad's good health fell off a cliff very suddenly and their lack of planning became apparent. The actual healthcare my dad received was good but what they lacked was the emotional support. There was an expectation that I'd be there on a monthly basis which just wasn't possible so we all started to resent each other.
Mum has been extra needy since dad died. She is determined to keep living there and, to be honest, doesn't have a choice - for reasons set out by others on this thread, she is unable to find somewhere to live back in the UK. So she wants to make the most of her life there but she also wants to live as if I'm just around the corner.
For everyone who thinks it's great to have cheap holidays on tap, the other way of looking at it is that my choice of how to spend holiday time has been totally removed for my entire adult life. The place my mum lives is not served by cheap, nor frequent flights so I have to set aside £8k per year to visit 2-3 times, which is the minimum I can do, yet she expects more. I have severe wanderlust and would love to visit other places but I don't have the option to do that. it also means there is never a break in my life, which has become more true as my parents became older and more dependent. I work in a stressful job and would love some downtime but pretty much all my annual leave is now spent caring for my mum and navigating Greek bureaucracy. There's no mental/emotional let up in my life and my mental health is suffering. As mum has gotten older, there's also very little chance of actually enjoying the island - we don't visit beauty spots or tourist sites, we don't go to the beach or eat local food; we spend the time helping her around the house.
In short, I'm not saying don;t do it. If this is what you want and the alternative is living a life of regret then you absolutely should. You need to consider everything carefully though - the bureaucracy that others have mentioned but also other practicalities: How many flights per week to your chosen location? What would be the cost? Is it likely that any of your children will move for work or otherwise - if so, how will that affect their ability to continue to visit you, or for you to see them on visits back to the UK? How would you genuinely feel if you go 1 year, 2 years, 3 year without a visit from one of your children? Would you resent them if they say that this year they are taking their kids to Disneyland instead?
Realistically, you need two plans: The first to cover your mid-50s-70s, and then a second for the next 20(ish) years. In my experience health drops off dramatically around 80 years old so perhaps plan for a life abroad for the earlier period and then something more practical afterwards? Or stay abroad but with everything meticulously planned.
And I can't stress enough, the importance of keeping a UK base.