At that point, why not just take the next, logical step and remove any reference to a 24-hour day at all?
I'm not being facetious.
For me, there are two reasons.
First is that they used the term rest. Seems stupid, but it makes a difference to me.
Second, because I think that there
should be a time element to regaining abilities. At least certain abilities.
Naturally, I've changed things a bit. Multiple times.
I view magic as requiring a sort of inner well of magical power. It doesn't decline over time, like fatigue doesn't alter it. Instead, that bit of magical energy, that attunement, is gone after you cast it or use an ability tied to it. You do have a limited amount you can "hold" at a time. A good night's sleep replenishes it (in my game it's sleep). But there's also a gradual natural replenishment. Which means if you don't sleep, that spell slot will become available to you again in 24 hours from when you used it. In reality, I track time in 4 hour blocks (early morning, dawn, morning, afternoon, evening, and night). So if you use it in the morning, it's available the next afternoon.
I have sleep separated into 2-hour periods (1 hour for reverie), so you can regain some of your spell slots, Hit Dice and hit points over a shorter period of sleep.
Any long rest ability works the same in my campaign, as most of them are (or could be) magically based.
Short rest abilities are a bit more challenging (for me, since I like an in-world explanation for how they work). I've landed (for now) on the idea that I don't really care if you have them for every encounter. So each rest (short or long) replenishes them. A (short) rest in my campaign is 10-15 minutes. I currently don't have warlocks or monks in my campaign, so it sidesteps the issues with regard to Ki or regaining spell slots for now.
You can also prepare spells any time you want, and you can change your prepared spells as well. It takes 15 minutes + 1 minute per level of spell slot to prepare.
Hit point recovery is automatic. After sleeping (and only sleeping) you recover all of your hit points, and 1/2 your Hit Dice (rounded down, minimum 0). You roll them and add your Constitution modifier as normal, and these are your hit point pool. Whenever you are performing non-strenuous activity, or resting, you regain hit points from this pool to your hit point maximum. Any magical healing, healing due to the use of a skill or ability is applied first, and hit points from your pool second. At some point during the day, your pool runs empty.
I'm considering tying the recovery of short rest abilities to the hit point pool. When it's empty, you can't regain short rest abilities. But I'm not that concerned about it because I have numerous conditions that use a modified exhaustion track, and that is not uncommon. So there's a good chance each day that you might not be 100%, but not every day. This can occur due to damage, or activity (such as climbing, swimming, or even combat) that are very strenuous.
So, what if they decide they want to take a nap in the middle of the day? Well, to start I have a quality of sleep rule. If you're uncomfortable (sleeping in armor, for example), then you subtract 15 minutes from each hour. If you are woken up, such as for combat, it costs you 30 minutes. (I also have a trait for somebody that can sleep anywhere, anytime, and ignore these penalties. You roll for traits randomly).
While I don't have a specific rule for it, if you're not tired, then it can be difficult to fall asleep. Your attempt might fail. If you're suffering from exhaustion, probably not. If you're fatigued, it might be more likely you can fall asleep. Otherwise it's one of those judgement calls. In most cases the answer will probably be no, you just can't fall asleep (unless you're one of the lucky, although I also have rules for perception in sleep, and waking up, and they have a harder time with that). It's of limited use anyway, since 2 hours of sleep regains 1 level of exhaustion, and 1/8 of your maximum hit points, Hit Dice, and spell slots, all rounded down (minimum 0). So a short sleep is of limited restorative value.
I'm sure the majority of people won't like my solutions. But they work together in a way that makes sense to me. Most of the time, all of these variables are irrelevant. Most of the time people just set up camp, and sleep at night, and the standard long rest rules are pretty much the same. The major difference is really the hit point pool, and the fact that I have conditions that make worrying about when they recover abilities and hit points irrelevant to me.
Why so many rules? Because I like things to make sense (to me), so I think through these sort of things anyway. But also because I like consistency. Things that I can easily quantify in a rule, I like in a rule. That way I don't
have to make a judgement call during the game. Like "I've been awake for 4 hours, can I take a nap?" There are a lot of variables there, and while I can write a rule and quantify all of that, the answer isn't consistent enough to write a simple rule. More importantly, there are some rules that I don't want a set answer, and this perhaps is one of them. It's a decision I want to leave open for me.
For those that don't like that approach, I'd probably recommend a 10% chance to be able to sleep for a 2-hour block for every 2 hours you've been awake, +5% for each level of fatigue/exhaustion. In d20 terms, that might be a DC 20 check (no modifiers), after being awake for 1 hour, -1 DC for each additional hour you are awake, -1 DC for each level of fatigue/exhaustion, -1 DC for each hour of sleep less than 6 in the prior night. You'd have to make that check for each 2-hour block of nap, with new modifiers due to the new sleep. Probably a +2 to +5 to the DC.
That's an awful lot of rule for something that will come up so infrequently, but I think it models what I'd like fairly well. Or I can just internalize it and wing it. It does show my thought process on what I might consider when I say, "no."