I think that if you have a free society and want to bother with justifying conscription (as opposed to some totalitarian shithole where the government does it because it can, it's cheap, and it works, like the levies of old, simple as that) it pretty much requires an invocation of nationalism or something related, based on the idea of the population's insistence on being independent, sovereign and self-governing, in turn implying basically a modern variation on the ancient idea of defending one's tribe. And in that tradition, there was no obsession about *everyone* taking part, more everyone capable of doing it.
What's outside of the tradition is the nature of modern warfare - requiring fairly expensive and long training, that can vary massively in cost. requirements and time depending on the position. Something like England's longbow training mandate is the closest i think, but even that works for something like territorial defense more than typical conscription.
As for exchangeable civil service, it's a rather mediocre solution without a problem, in fact communist countries practiced a lot of similar things for various reasons, but the obvious problem is that it gives the state a shitload of free manpower with limited motivation (everyone doing the bare minimum for the service to count, why bother with trying anything beyond that, service done is service done) and varying but generally not great skills, which means "lowest common denominator" work, make-work, favor trading...
Or in other words, it promotes corruption, waste and inefficiency in functioning of the state, as if we didn't have enough of such problems without this.
Not to mention that even then, in terms of sacrifice and risk that compares only to peacetime training, wartime service as a conscript doesn't really compare properly, which would raise an issue of unfairness.
Still conflicted about it : if they offer like something free stuff (like many sections of the Italian Army DO) or like the USA with college, you could make military conscription mandatory but give something to alleviate this.
That's just payment with extra confusion, bureaucracy and room for political shenanigans. I think most of soldiers getting those benefits, if they had the option that at the end instead of these benefits they will get a lump sum of money equivalent to their value, they would rather have that.