I can't see the 3I, at least in peacetime--or for that matter any larger polity--wanting to draft individuals from low tech worlds with low levels of education. What good to a TL 12 let's say military is someone who grew up with TL 5 and barely can do simple algebra, doesn't understand half the words in a tech manual, and has never seen anything close to TL 12 technology? The military would spend several years just teaching someone like that enough basic skills to make them trainable. Why waste the time?
They might well still get drafted into the local planetary military, though (however, the draft rules don't cover this distinction). And I could see the Imperial services being required to accept a certain number of people from low-tech worlds as part of a half-assed technology uplift program (train people, hope than when released they'll go home, taking their skills back with them), but that would probably not be drafted individuals - which is amusing because the draft ignores any homeworld requirements in
MT (where homeworld is first made a consideration for standard chargen).
If keeping the draft and having it make some kind of sense is important, I'd make it a hold-over from the early Imperium.
Originally a requirement for member worlds, to provide the young Imperium with manpower, hostages, and so that a segment of the population would be exposed to new worlds and cultures, and (hopefully) instilled with a sense of belonging to, and loyalty to, the Imperium as a whole and not to just their homeworld.
In later times it remains as a tradition, and is held to still have value for the last features - broadening the horizons of the draftees. So each member world is obliged to provide the Imperium with a draft of 18-year olds each year, and the Imperium is obliged to take them and employ them offworld.
The details differ here depending on edition. In CT they end up in an Imperial service, barring a few who get handed off to merchant shippers, and a few others who slip through the cracks and end up doing... something.
In MT the draft always puts you in Imperial service, most often in some kind of planetary military role (army, COACC, wet navy), which suggests that this 'broadening of the horizons' might quite often mean 'some military base on some shit-hole world different from home only in that it's not home'.
MgT allows to possibility of ending up in the merchants, but otherwise it's Imperial service. However, it's also not limited to 18-year olds, so rather than 'the Draft' being 18-year olds, it's 'adults of sound mind and body' (with a loose definition of 'sound'), and I'd guess some worlds just dump any unemployed that meet the medical requirements and don't seem to have useful skills into the Imperial Draft system.
I think that vaguely works. It's probably not going to be a major part of a campaign anyway.