I know someone who did this. First of all, it’s slightly illegal because you are going from country to country on a tourist visa — but you’re actually working in the country.
Secondly, the housing the company provided led to some issues. What they don’t tell you outright is that you hardly ever get your own place; you always have to share with at least one and even quite a few other “flexpats”.
As you might expect, not everybody shares the same concept when it comes to “flexpatism”: some want to live an extended hedonistic Spring Break, while others actually want to work while indulging more quiet pastimes and finding ways to connect with the local culture.
Also, it seemed crazy expensive. You can do the same thing but figure it out for yourself with a good flight aggregator and AirBnB.