I agree with what Rachel has said as far as it being okay to respond to Thank you
with Thank you
, but I think the interpretation of possible arrogance is perhaps a bit much.
To begin with, a suprasegmental feature may be necessary to hear to know what's being communicated by the respondent, i.e., where the stress falls. For example:capitalized elements receive primary stress
Izzy: THANK you very MUCH, Rachel.
Rachel: Thank YOU, Izzy.
In the case above, Rachel is politely returning the compliment, so to speak. She is being as gracious as Izzy is, and she clearly demonstrates this by emphasizing you
I'm sure that Rachel is right in citing that when the respondent simply repeats Thank you
with the same stress as the first speaker, the part left out but understood is something like "... for having me on the show" or "... for interviewing me."
As for the respondent perhaps demonstrating some kind of arrogance by saying You're welcome
, I can't really agree with that. On the radio, for example, after a news report, I've heard the reporters respond with You're welcome
as often as with Thank you
to the news anchor saying Thank you
, and there isn't a hint of arrogance in their reply.
That's my take on things.