Robert Swinney wrote:

There's no "big deal", except that the curt, "thanks in advance" has a ring
of finality to it, IMO. Again, and IMO, it is less "put-offish" to use no
closing at all.

Sounds pretty anal to me. I'm sure with a bit of effort you can find
something to complain about in any message.

I use TIA when to indicate I'm really looking for an answer especially
when the question could possibly be interpreted as critical.

Ted