I was under the impression that all 'breadbox' C=64s (as well as all of the SX-64s) used the 6581, and that all of the 'wedge' C=64Cs (as well as all of the C=128/D/CRs) used the later 8580 (also known as the 6582).
Not always true. I have a C64C that uses the original 6581 SID chip, and the later breadbin-style C64s sold in Europe (the "C64 Aldi" and "C64G") use the 8580 SID chip.
Wikipedia is only as good as the information provided to it by users. That being said, 6581's in various revisions were the most common SID, the 8580's being found in late C64C's and C128DCR's.Wikipedia does say that some early 64Cs used 6581 SIDs instead of the 8580, but doesn't say anything about the other chips, or the overall board layout.
Did any of the older wedge C=128s use the old-style SID chip?
That makes sense. When I cracked open my C=64C, I noticed that the only ICs which were socketed were the SID, the VIC II, and one of its associated 14-pin ICs (not sure of the designation). Though the date codes of the chips in mine are all fairly close, I could easily see an amateur repairer swap out the socketed chips as a first test, find that the problem still persisted, and then leaving the newly-swapped-in ICs in place as they dug up a soldering iron to attempt some 'deeper' repair work...Not only did C= use whatever was on hand, in my experience it wasn't uncommon for users to replace them. And you never knew what the local computer shop would stock.
Most of the time, the SID didn't even need to be replaced, the PLA was the problem.