During the pandemic, a number of states instituted hold-harmless funding policies to protect school district financially from declining enrollments. In addition, some school choice policies have protected traditional public schools financially from declining enrollments. Together, these policies raise the question of whether competitive effects can exist in a policy environment of reduced financial pressure. Theoretically, despite the lack of financial pressure, schools could feel competitive pressure in other ways including a loss of reputation as students move to schools of choice. To provide insights on whether schools can improve without the threat of financial loss, we examine the Seoul school choice program which introduced autonomous private high schools (APHSs) in the context in which there is equalized funding across schools. More specifically, we examine whether competition induced by APHSs affects the achievement of students attending traditional public and private schools. The effect of APHSs is identified by exploiting plausible exogenous APHSs' entry through the random assignment of students. We find a small and positive effect of APHS penetration on the Korean and English achievement of private school students while finding no effects for traditional public schools, which have limited ability to respond.