It easy to move staff from the officeA to the officeB in the same city, in fact I witnessed such moves multiple times. However moving from AWS to Azure is not that easy at all!

This analogy doesn't really apply because thanks to bandwidth charges, it's uneconomical to have a 2-bed house (outside of the cloud) and occasionally rent the 8-bed in the cloud, so you're forced to also get the 2-bed one in the cloud and pay insane margins on that too.

Extending this metaphor, I would then want to own my two bedroom home, and take a vacation to the rented mansion.

Is there a well trodden way to serve most of your everyday traffic out of your own datacenter, but scale out to cloud infra when traffic peaks?

the buying vs renting calculus depends on the respective prices and rates. now think what happens if the entire rentable stock of housing was owned by three companies.