Submarine aircraft carriers and SSGNs

Could a submarine aircraft carrier actually be built, and what would its role be?

The concept was most plausible before and during World War II, but modern SSGNs perform the strike role without the aircraft-recovery burden.

Aircraft-carrying submarines were tried at several points before and during World War II, when the concept reached its peak. The comparison treats them as the equivalents of the later SSGN. SSGNs remove the need to reproduce that aircraft-carrying complexity. Recovering the aircraft is the particular difficulty identified for a submarine carrier.