random effects specification

which I presume is due to the fact that the data are unreplicated,
i.e. individuals get each treatment only once.

No. Due to not having a random component for id in the simulated data.

Try

rid <- rep(rnorm(20),each=3)
dta$n <- dta$n+rid

Then refit the model.

Are there any gotchas in
the interpretation of the results after this warning?

Probably not, but with real data I would remove the random effect from  
the model as it is 0.

Ken