Why can't I find cheap TQFP 44 sockets?
My suggestion is don't use a socket.  TQFP packages are intended for surface mounting, not socket use.  Clamshell type sockets do exist, but they are expensive due to being complex and because of low volume.  I doubt you'll find one that isn't at least several times the cost of the microcontroller you are trying to put in the circuit.

Why do you think you need a socket?  There should be no need to replace a microcontroller on a board once mounted, and nowadays with in circuit debugging that is not a reason for a socket either.