The examples you gave were either deposed through a revolution, or lost power because the former monarch chose the wrong side and was seen as complicit in leading the nation to ruin. If the populace was upset enough to end royal rule, why would they tolerate a reminder of their unhappy past living lavishly in their midst?
The British monarchy, which you mentioned, is a case where the king gradually lost power through ceding it to parliamentParliament. There was a somewhat amicable transfer of power without lasting bitter feelings among the public and political classclasses. This facilitated the idea of a 'constitutional monarchy' in which the nation has a sanctioned figurehead who also serves as a reminder of their glorious past, while the actual decisions are made by a democratic caucus.
Some of the reasons to exile ex-rulers (kings, dictators, even PMs out of political favor) are:
- Prevents them from rebuilding a network of loyalists for a possible counter coup.
- Prevents discussion on the legitimacy of the incumbents especially when the transfer of power was disputed.
- Removes an unnecessary drain on the state exchequer.
- Security considerations, especially if the ruler was greatly disliked in public.
- They may simply exile themselves out of shame at losing their position or to avoid conflict.