Meaning of the "why not" modality from linear type theory?
First off, one thing I'd recommend is reading Filinski's Linear Continuations for ideas on how to interpret linear connectives (note, the ? modality got typeset as Γ in that for some reason).

In that paper, he uses the modality as part of the interpretation of call-by-name into linear logic. The idea is that you can kind of think of the non-modal types $T$ as being total, while $?T$ adds the possibility of divergence. If you want an analogue of "infinitely many copies of $T$", then it's, "zero or one $T$".

But of course, it's not like $1 + T$. It's more like a partiality monad living in an otherwise total language.