It's certainly not something that people believed and built stuff on the basis of; it was never regarded as anything more than a conjecture and I would be a little surprised if even one paper was published that took the conjecture as a hypothesis, even explicitly (i.e., "We show that if Euler's conjecture is true then ...").

It's also not, so far as I know, a case where anyone reacted with defensiveness, horror, insecurity, etc., when a counterexample was found. They published a paper in a reputable journal. They don't seem to have had much trouble getting it published, if they discovered the counterexample in 1966 and the paper was published in a 1966 issue of said journal.

So if you're suggesting that this is a case where "people were building on swathes of mathematics that seem proven and make intuitive sense, but needed formal buttressing", I'd like to see some evidence. Same if you're suggesting that this is a case where "so-called experts had invested far, far too many of their man-years in that unproven conjecture" and there'd be a hostile reaction to a counterexample.

On the other hand, if you're not suggesting either of those things, I'm not sure what the connection to the rest of the discussion is.