One reason for using less flap in Cessna singles in a crosswind is to avoid landing nosewheel first which can do bad things to the firewall.
In the C172 I fly there is a placard saying:
Avoid slips with flaps extended
The POH goes into more detail:
When landing in a strong crosswind, use the minimum flap setting required for the field length, If flap settings greater than 20° are used in sideslips with full rudder deflection, some elevator oscillation may be felt, at normal approach speeds. However, this does not affect control of the airplane. ...