No, it's not the standard world wide. For the simple reason that consuming that much water and energy (to heat the water) costs a lot of money. And most people in the world don't have that much money.

In some places (e.g. Central America) they do use cold water to shower. Might be hard in cold climates though.

The implication was not. I can really only speak for the UK/US, barring anecdotes I hear about the Paris Metro.