At mouser.com:
tip122 $.050
pn2222 $0.06
NTD4963N (mosfet 44A, 13.9mOhm) $0.19 (this is a great bargain)
So, no, the tip122 is not the cheapest solution.
And if you want to go surface mount, there is:
NX3008NBK,215 (mofset, SMD, 400mA, 1.4Ohm) 0.05
Bob