I've operated recip engines lean of peak from small displacement engines to large radials...each with carburetors, sometimes fully outfitted with individual cylinder instrumentation, sometimes not. And yes, it really can be done. Just not by you, it would seem. By thousands of others...yes. But not by you. And that's okay...because nobody is forcing you to operate that way, and you don't need to do so.
You misunderstand me, SNS3Guppy. I have been quite happily operating an IO-550 lean of peak for many years, but that of course is fuel injected.
My knowledge on operating the carburetted Lycoming and Continental flat fours and sixes LOP stems largely from the feedback from a very large number of graduates of the Advanced Pilot Seminars on Engine Management that are run by Walter Atkinson, George Braly and John Deakin. If you've no objection, I'll take that very large sample size any day over your sample of one!