As a CFI, I don't like touch-and-goes because they tend to reinforce bad
habits. Specifically, during a touch-and-go, you need to retract flaps
before you add power. This is TERRIBLE reinforcement for go-around
procedures. I have often done BFRs for pilots who learned using T&G's, and
when asked to go around they almost always retract flaps before adding
power. This is very bad. My home field is relatively short, too, so I don't
do T&G's with my students.

Why do you have to retract the flaps first when doing a T&G?

Because Cessna-172s don't take off very well with full flaps. I suppose you
could add power and then retract the flaps, but then you're rolling with
lots of drag and runway behind you is useless. In any case, it seems to be
conventional to retract-then-power when doing T&G's, and that produces bad
habits.

Only those Cessna's with 40 degrees of flaps may be unable to climb.
Cessna's limited to 30 degrees of flaps can and will climb with full
power. You have to know how to "milk" the flaps up as airspeed increases
to fly properly, though.