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The primary sense of the word "at" is spatial: it mainly indicates a location without regard to its structure. You say "I am at work" or "I work at 10th St. and Main" when you just mean the location; you say "I am in the building" when you want to distinguish being inside or outside. My answer here gives more details. The main thing to notice is that "at" tends to suggest that you are regarding a location as a point in space even if really it's larger than that.

The succession of "at"s establishes that each time is the start time for an activity. "At" is appropriate because the schedule doesn't describe what happens inside each activity. So, a reader is less likely to notice that "sleep at" would be unusual in other contexts. Proximity agreement is another situation where people often don't notice that a norm has been violated, because some other, more-salient factor drowns it out.

The primary sense of the word "at" is spatial: it mainly indicates a location without regard to its structure. You say "I am at work" or "I work at 10th St. and Main" when you just mean the location; you say "I am in the building" when you want to distinguish being inside or outside. My answer here gives more details. The main thing to notice is that "at" tends to suggest that you are regarding a location as a point in space even if really it's larger than that.

The succession of "at"s establishes that each time is the start time for an activity. "At" is appropriate because the schedule doesn't describe what happens inside each activity. So, a reader is less likely to notice that "sleep at" would be unusual in other contexts. Proximity agreement is another situation where people often don't notice that a norm has been violated, because some other, more-salient factor drowns it out.

The primary sense of the word "at" is spatial: it indicates an object that you might aim at, and especially a place without regard to its structure. You say "I am at work" or "I work at 10th St. and Main" when you just mean the location; you say "I am in the building" when you want to distinguish being inside or outside. My answer here gives more details. The main thing to notice is that "at" tends to suggest that you are regarding something as a point in space even if really it's larger than that.

Stretching sleep and at to make sense with each other

The primary sense of the word "at" is spatial: it mainly indicates a location without regard to its structure. You say "I am at work" or "I work at 10th St. and Main" when you just mean the location; you say "I am in the building" when you want to distinguish being inside or outside. My answer here gives more details. The main thing to notice is that "at" tends to suggest that you are regarding a location as a point in space even if really it's larger than that.

Stretching slept and at to make sense with each other

But probably the more important factor here is that a routine is a plan, not an actual series of events. A plan is an idealization, which exists only in your mind. So, in your mind, as you plan out your routine, you imagine that you start sleeping at precisely 10:00, just as your meeting starts at precisely 9:00. In an idealization, you think of activities as starting at precise, known points in time even though you know they won't go exactly like that in reality. If you say "Last night, I slept at 10:00", this is a little strange, because it suggests that you know precisely when you fell asleep, and in reality, that doesn't happen.

But probably the more important factor here is that a routine is a plan, not an actual series of events. A plan is an idealization, which exists only in your mind. So, in your mind, as you plan out your routine, you imagine that you start sleeping at precisely 10:00, just as your meeting starts at precisely 9:00. In an idealization, you think of activities as starting at precise, known points in time even though you know they won't go exactly like that in reality. That makes "at" a very good fit. But if you say "Last night, I slept at 10:00", this sounds strange because it suggests that you know precisely when you fell asleep, and in reality, that doesn't happen.