I know that 5-HT2A partial agonism is the key mechanism of action of serotonergic psychedelics but I also know that some research (e.g. the selective (no activity on any other known receptor sites) 5-HT2A inverse agonist/antagonist eplivanserin was being investigated as a sedative) says that central blockade of the 5-HT2A receptors induces sedation which is in opposition to the effect of 5-HT2A partial agonists.
I have a partial answer to my question. I heard from LSD users that they find it regularly causes sleeplessness for the duration of its effects, which is likely due to stimulant/wakefulness-promoting (eurogenic) effects. Albeit just because it is true for one serotonergic psychedelic doesn't necessarily mean it is true for all serotonergic psychedelics. Especially since LSD affects a wide range of serotonin and other receptor subtypes.