Well, interestingly enough - melatonin has important functions which are triggered alongside sleep. It appears to run a nightly "metabolite reset" process, which continues during sleep and allows you to feel "refreshed" the next day. I'd consider a failure of this process as being a cause for ongoing PEM, even in non CFS/ME people, if chronic.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4334454/Now.. tryptophan can be scavenged to make Acetyl-CoA (both issues in this disease model)
Likewise N-Acetylserotonin needs acetyl-CoA again (likewise an issue)
..and you need darkness to stimulate melatonin synthesis, so lights, screen time, etc., are not helpful.

Now, it's possible, that someone could take vast amounts of melatonin and potentially force these cleanup routines to run all day..
however they'd likely be falling asleep all day. It's possible that by countering that with some common anti-narcolepsy drug or vast amount of exogenous thyroid hormone, you could potentially counter this sleepiness effect, with favourable results overall and a handful of side-effects. (Chatting with Learner1, she has some really good info on this topic, which I hope she'll contribute.)
My view is that trying to restore the cells to their normal operating conditions is the optimal way forward.
I included a 300mcg dose of melatonin in the v2 and v3 protocol to assist with maintaining sleep, where these pathways are not optimal.
I've recently seen a 6 hour slow-release melatonin product, which drip-feed 300mcg, 750mg or other amounts of melatonin over that period. For unusual cases / unresolved co-infections, this could be helpful, however would need further testing.