If it even worked the way I imagined it, slotting for Sleep would become a lot worse. Let's take a Sleep that currently lasts 15 seconds. If we converted it to Sleep-over-time (if that's even possible), it would become something like 5 ticks of 5-second sleeps, over 10 seconds. Unslotted and uninterrupted, that would still last 15 seconds. However, with 100% sleep enhancement, the original version would last 30 seconds, while the Sleep-over-time version would last only 20 seconds. So it'd be a buff in one way, but a nerf in another.
Then the question would be why bother with it at all? Players that use and slot sleep likely get their money's worth and this is only pandering to players who already have a full course of other control options available. This is in a similar position (although not as hotly discussed) as knockback. At best, such a suggestion would be best implemented as some sort of trade-off option like a slot enhancement that might cast sleep on the target again.
Something not mentioned regarding sleep is how it is stacked. Blaster Frozen Aura is one of those sleeps that don't cause damage thus it can actually stack with other sleeps to put resistant foes to sleep. Personally, I think an easy QoL fix for Sleep effects would be removing "damage ends the effect" and just have the magnitude remain but the effect suppressed. You could then create some sort of effect where if the target doesn't act (use their endurance), they can fall back to sleep if the effect hasn't expired.
Why bother? Because it makes Sleep a more reliable method of control. It wouldn't be appropriate for every sleep power, but I think it would work well for Frozen Aura.