A 24 hour towered airport could still have a published ODP in the event the radar goes out.

Seems to me a SID of for ATC convenience. ie, they don't have to tell you the freqs / alts / routing if it's depicted and therefore makes their job easier.

An ODP, on the other hand, is simply to get the aircraft from the runway to the enroute structure without hitting dirt along the way. It's not for ATC, it's for the health of the pilot and pax.

I would also imagine that both SIDs and ODPs have to comply with the same climb gradient / terrain clearance requirements in the TERPs, but I could be wrong there. Just a hunch.