Willingness is the wrong thing though.
It's about whether you can consciously cause your body to do something or not. Humans (and we can assume most humanoids in D&D) have limited control over their bodies. Like, we can't intentionally stop or start hiccoughing (generally - I had a bizarre ability to stop hiccups with a thought, 100% reliably, for like 6-7 years then it went away). We can fake a sneeze, but you can't make yourself actually sneeze (well, most people can't anyway). Nor can most people puke without getting some fingers in their throat etc. Whereas you can cough, or laugh. But what about a backflip, say? I'm pretty sure most DMs would rule that telling an NPC to backflip with command would cause them to ATTEMPT a backflip, not to succeed at a backflip.
And that's the problem here. There seems to be an assumption of success with sleep that doesn't really make any sense. If you're commanded to "Sleep", then I'm sure you'd try to go to sleep - you'd spend six seconds trying extremely hard. But why would you succeed?
That's the question? Why would there be autosuccess here and not with other things?
I think, if you're consistent, and all other Commands are always successful - i.e. "backflip" makes them actually perform a backflip if it was even physically possible, even though they couldn't do it consciously, "splits" has them close to the floor as possible, perhaps even to the admiration of Jean-Claude Van Damme, "burp" makes them burp even though they didn't have any wind to do it with, and so on, then sure, it makes sense for sleep to make them fall asleep. But if you're running it as causing the creature to attempt, completely wholeheartedly, to do that thing, whether or not they can actually succeed, which is how I've usually seen it run, then I don't think "sleep" should actually send them to sleep. It might still break concentration, depending on the DM, because they'd genuinely be trying to get to sleep, and I'm pretty sure that involves stopping concentrating on spells, but unless other Commands allow you to speak directly to the involuntary nervous system, I dunno why this should.