The direct detection of core-collapse supernova (SN) progenitor stars is a powerful way of probing the last stages of stellar evolution. However, detections in archival Hubble Space Telescope images are limited to about one detection per year. Here, we explore whether we can increase the detection rate by using data from ground-based wide-field surveys. Due to crowding and atmospheric blurring, progenitor stars can typically not be identified in preexplosion images alone. Instead, we combine many pre-SN and late-time images to search for the disappearance of the progenitor star. As a proof of concept, we implement our search of ZTF data. For a few hundred images, we achieve limiting magnitudes of ~23mag in the g and r bands. However, no progenitor stars or long-lived outbursts are detected for 29 SNe within z<=0.01, and the ZTF limits are typically several magnitudes less constraining than detected progenitors in the literature. Next, we estimate progenitor detection rates for the Legacy Survey of Space and Time (LSST) with the Vera C. Rubin telescope by simulating a population of nearby SNe. The background from bright host galaxies reduces the nominal LSST sensitivity by, on average, 0.4 mag. Over the 10 yr survey, we expect the detection of ~50 red supergiant progenitors and several yellow and blue supergiants. The progenitors of Type Ib and Ic SNe will be detectable if they are brighter than -4.7 or -4.0 mag in the LSST i band, respectively. In addition, we expect the detection of hundreds of pre-SN outbursts depending on their brightness and duration.