Rust does not affect the crown, so if you've removed all the leaves right down to a bare crown, then unless any spores remain in the environment and there is new growth that starts before they die, the rust should not persist. Whether or not you might want to apply a fungicide as well would depend on the individual situation. See this web page:
http://web.ncf.ca/ah748/newpla...
Rust should not survive the winter where you are.
Almost all the problems listed have been around for years, Stout wrote about thrips on daylilies, spring sickness has been around since at least the 1940s, I forget when leaf streak was first noticed (I think it was by Spencer and it had a different name back then). I doubt shoestring root rot is very common in daylilies, it only occurs in certain environments, such as old orchards or where there are other infected woody plants.
We don't know if TRSV (tobacco ringspot virus) occurs in North American daylilies, it was intercepted on imported daylilies. Presumably it is likely but you would see the spots.
The biggest concern in Ontario right now, IMHO, would be the daylily gall midge. Like daylily rust and the daylily leafminer, these are recent imports from overseas that somehow got past the phytosanitary requirements.
