New ceramic over old in bath remodel?

Greetings,
We are in the process of interviewing contractors for a gut/re-do of our small bathroom. Everything in the bathroom is being removed -- tub, sink, toilet, door and trim -- and the walls will go down to the studs.
Currently, the floor is 1950s vintage small tiles, an interlocking design of flat, matte pieces about 1-1/2 to 2". Other than being unattractive it's in good structural condition -- nothing loose or shifting. Truth be told, it's the best thing about the bathroom at this point in time. :/
The first two contractors have said they would tile over the old floor rather than remove it. Is this advisable? With the tub being removed there's no way that joint will match -- how does that get handled properly?
Thanks, Hera
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snipped-for-privacy@msn.com wrote in message

It can be done. We had two bathrooms redone about 4 years ago and they look good. TB
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