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We present a simple time-dependent model of viscously spreading accretion disks around black holes (BHs) with masses ranging from 10−108M⊙. We apply the results to observations of late-time emission in tidal disruption events (TDEs) and luminous fast blue optical transients (LFBOTs) such as AT2018cow. Our model generalizes previous work by incorporating outflows during phases of super-Eddington accretion, non-conservation of mass and angular momentum in TDE circularization, irradiation of the outer disk by the inner accretion flow, and a range of viscous stress models. We show that many of the late-time plateaus in TDEs can be explained by disks that form with a large spread in angular momentum, due to angular momentum redistribution during circularization. Viscous spreading on year timescales is not required, although it is also compatible with the data. The significant range of peak TDE X-ray luminosities is also consistent with a range of disk spreading timescales. The collapse of radiation pressure dominated thin disks to the stable gas-pressure dominated phase underpredicts TDE plateau luminosities by orders of magnitude, strongly favoring thermally stable magnetically dominated disk models. Irradiation of the outer disk in TDEs due to misalignment of the stellar orbit and BH spin increases plateau luminosities and durations by factors of a few. Continued study of late-time TDE emission provides a unique opportunity to constrain the physics of disk formation and circularization, accretion disk warps, angular momentum transport, and other poorly understood aspects of disk physics. The models developed here can also explain the late-time optical-UV emission in the LFBOT AT2018cow for BH masses of ∼10−100M⊙. The very faint X-ray emission at late-times in AT2018cow is likely due to ongoing X-ray absorption. Our models predict that late-time X-rays at should eventually be detectable (again) in LFBOTs and that HST-JWST observations of AT2018cow may detect a break in the SED at near-IR-optical wavelengths, providing a powerful probe of the outer accretion disk thermodynamics.