Substance theory is closer to what most religious doctrines of an immortal soul or an enduring self actually require than continuity theory is, since a doctrine of resurrection or rebirth generally wants to say that the very same person, not merely someone psychologically continuous with them, persists through death and beyond, including through the total discontinuity of memory that death, on most such doctrines, involves; this is precisely why substance-based accounts of the soul have historically been the default in traditions asserting personal survival, even where the philosophical vocabulary of substance and accident was never explicitly invoked.
The theory's own persistent weakness is less logical than epistemic: a substance that can, in principle, persist through total psychological discontinuity is, by the same token, extremely difficult to verify or even to make sense of empirically, since nothing observable, no memory, no character trait, no bodily continuity, is strictly required by the theory to track it, leading critics to charge that positing such a substance explains identity only by placing it beyond any possible evidence either way. Continuity theorists reply that this is exactly the theory's problem rather than its virtue, an unfalsifiable posit standing in for a genuine explanation, while substance theorists answer that some questions, including whether the person who wakes up tomorrow is really you, are simply not the kind of question empirical evidence alone was ever going to settle.