Is it normal for Starfleet to provide replacement ships?

I was reading a Star Trek post here, and was reminded of an oddity. When Kirk lost the Enterprise, Starfleet gave him and his crew a shiny new Enterprise A. When Picard lost the Enterprise D, something similar happened and he and his crew got a shiny new Enterprise E. When Sisko and crew lost the Defiant, a replacement was provided to them as well, but they didn't tack a letter on to it.

This seems really peculiar to me, as I'd think the loss of a ship would definitely not result in the replacement for that ship being handed right back to the people who necessitated the replacement. But, here are three notable examples.

Is this normal Starfleet/Federation procedure; to grant survivors of a lost ship a replacement?