Single, multi-, double-sided or spectral coatings...whatever is there or not will not be helped by placing a filter, or several filters, on the front of the lens. Filters today are several orders of magnitude greatly more effective in dealing with flare on either or both sides of the filter; they are often a good choice for hedging the menace on old lenses with known predisposing factors to flare or image degradation from contrasty light sources.
It depends on the quality of coatings, and single coated is a misnomer as some coated (pre-MC) lenses have more than one coating layer. Another fly in the ointment is some manufactuers skimp by not coating every air/glass surface.
Let's start with the worst case. Hoya MC lenses, flare was so bad they scrapped the entire range and went back to the drawing board and launched a new range under their Tokina brand name. They'd not coated some internal air/glass interfaces.
Ian, your post makes the most sense to me. I have no expertise in the field of optics, but it seems to me that coatings become more and more important as the number of elements and glass-to-air surfaces increases.
My old 135/3.5 (four elements, three groups) has single coatings and my slightly more modern 18/4 (13 elements, nine groups) has more advanced multi-coatings, but the earlier, simpler telephoto definitely packs more of a visual punch.
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