I have, by reading the various posts here, noticed that disturbing an animal that is sleeping in order to handle it is tolerated and even encouraged in this forum. Why exactly? Just because an animal is less responsive and perhapse slower due to low temperatures and light doesn't mean that it loves our attention. Such type of handling would no way be directed towards other animal species. Isn't it better to handle them at day, even if they are nervous?
Furthermore, there are predators in the wild that catch these animals while they are sleeping or resting. For example woma pythons catch eastern bearded dragons (Pogona barbata) in that way. We might frighten our dragons more than we do imagine. I am talking mostly about newly acquired animals, which have not been acustomed to human contact yet.
I don't think it's encouraged to bother a sleeping beardie; it's encouraged to handle them in the evening before they fall asleep, when they are more relaxed, but not while they are actually sleeping. But handling them when they are more relaxed is an opportunity to show them that you don't mean them harm and to let them get accustomed to your scent without eliciting a strong, distracting stress response - essentially a way to build up positive associations that may be difficult to achieve earlier in the day when a beardie is extra energetic.
Regarding your comment about other species, it is a concept that I would actually apply to other species, just in a different context. For instance, if I were to train a puppy to sit, I'd want to do it after he's run around some and gotten his puppy energy out because then he'll be more inclined to focus. Likewise, if I want to show a young beardie that handling is a good thing, I want to do it after the beardie has gotten the majority of his energy out so that he'll be more approachable and accepting of handling.
I agree that it's best not to disturb them if they've already fallen asleep, however, since it can cause them to wake up suddenly and misunderstand the situation (i.e. think you're a predator).
Baring in mind how much I hate being suddenly woken up and forced to get up if I was sound asleep.
I tend to wake my beardies, bluetongues and water skink gently if they are asleep when it's time to have a feed - in fact , since I feed all mine their insects once a day every day now (even though they are all grown mature adults lizards) , I'll sometimes just let them stay asleep , and so they'll miss out on that day's meal of insects - they make sure this doesn't happen the next day, and are eager for their dinner after missing a meal.... oh .... they know and make sure I know they know they know. LOL
By waking gently, I mean I'll lift the hide off from over them if they are in their hide and I'll simply start gently stroking them on the back and talking to them until they open their eyes and perhaps look at me , then gently scoop the still very relaxed lizard up and place him or her on my chest and give them a nice wakeup greeting of a snuggle and some petting.
This way I can avoid unnecessarily stressing the lizards on waking them up.
This is what I do with Rex , who is my livewire beardie . She'll trot about , exploring and generally getting into everything , until she runs out of steam and / or is satisfied everything is in it proper place and nothing has changed and then she will either crash and curl up somewhere in a corner and have a nap , or she'll (if she's in the mood) often come over right up to about 3ft away from me and stare up at me - I take this as her telling me "I'm ready for a cuddle now daddy, please pick me up".