||Gaps in protoplanetary disks have long been hailed as signposts of planet formation. However, a direct link between exoplanets and disks remains hard to identify. We present a large sample study of ALMA disk surveys of nearby star-forming regions to disentangle this connection. All disks are classified as either structured (transition, ring, extended) or nonstructured (compact) disks. Although low-resolution observations may not identify large-scale substructure, we assume that an extended disk must contain substructure from a dust evolution argument. A comparison across ages reveals that structured disks retain high dust masses up to at least 10 Myr, whereas the dust mass of compact, nonstructured disks decreases over time. This can be understood if the dust mass evolves primarily by radial drift, unless drift is prevented by pressure bumps. We identify a stellar mass dependence of the fraction of structured disks. We propose a scenario linking this dependence with that of giant exoplanet occurrence rates. We show that there are enough exoplanets to account for the observed disk structures if transitional disks are created by exoplanets more massive than Jupiter and ring disks by exoplanets more massive than Neptune, under the assumption that most of those planets eventually migrate inwards. On the other hand, the known anticorrelation between transiting super-Earths and stellar mass implies those planets must form in the disks without observed structure, consistent with formation through pebble accretion in drift-dominated disks. These findings support an evolutionary scenario where the early formation of giant planets determines the disk's dust evolution and its observational appearance.