I often chat to a Capuchin Franciscan friar and he tells me that in their tradition they consider themselves homeless and have to move monasteries every few years which to be honest doesn't sound all that much of an improvement on the current rental sector.

The difference is, he opted in! Certain religious communities are static, and in others it’s normal to move around. Franciscan Friers specifically promise not to be tied.

That’s specifically a Franciscan thing (and friars are not monks). Monasticism is about stability and you stay in the same community/ house unless something exceptional happens.