When phones are no longer considered reliable to make emergency calls in certain places, what alternative is there?

Sure it sucks for the operator to get a call, "Sorry, just testing to make sure emergency calling works, thanks, bye" and it would also suck, probably even more, for an individual to not be able to make an emergency call. Squeaky wheel gets the grease, hopefully someone improves the system, lol.

You can't just say A less bad then B so we should all do A.

You have to consider number of A * badness A vs number of B * badness B.

If thousands of pixel users start doing test calls in mass you will actually start causing that unable to make an emergency call issue.

Frequently calling the alarm number without a valid reason can be fined up to 6700 euro, or result in 3 months detention here.

So if Pixel still has this bug, that's just another reason not to buy a Google product.

What's the threshold by which a phone isn't considered reliable enough to make emergency calls?

I've never personally had an emergency call fail on a Pixel device, and I don't know the broader statistics of how often they fail for other people compared to other phones. Do you?

What I've done is write the dispatch center a friendly email explaining what I want and suggesting that they choose any off-peak time they find convenient.

A few days later, they called me and said that I could make the test call right now. Worked fine.