Yes, suede in summer is just as nice as in winter. From wingtips to loafers to drivers, all perfectly fine to wear in summer, though it does help if they're slightly lighter in shade than their winter counterparts.
Linen and cotton are both perfectly fine with it. I'd even say summer tropical wool suits are fine with suede shoes, but only if they're obviously casual (eg cream or similarly pale shade, not navy or most greys. Perhaps even exceptionally pale grey, beyond dove grey in shade). It may not be exactly traditional, but is certainly visually pleasing.
Flannel suit, esp casual flannel suit (OK, many flannel suits are naturally fairly casual, but I'm particularly thinking of ones with POW checks or similar) = perfectly fine with suede. A bit rogueish of a combination, but then the Duke of Windsor was a rogue, so OK. A fine look, esp. for a more casual day at work or a trip to the races or whatever.
Worsted wool business suits with suede shoes is an Italian thing, yes. I suspect it was hugely influenced by one or two of the better-known Italian style icons of the 60s adopting it after seeing American movie stars doing the look, after they started copying the Duke. With each stage of replication/propagation, the gap in formality increased (natural extension of a trend is to keep exaggerating it) until they ended up with perfectly normal/discreet business suits paired with suede shoes.
It's that specific combination that I find dislikeable. They're so obviously dissimilar items to me. I can certainly accept that others like it and as long as they enjoy it, good for them. But I can't feel aesthetic pleasure from seeing the combination.
PS. glad to have sparked some lively conversation about an actual style issue in this thread, rather than the more meta discussion that often happens! Nice work lads.