If automation implicitly increases wealth, why is it generally considered undesirable? When it comes to the subject of automation, I read that the wide majority of the arguments assume that the profits/savings "vanish", alongside the jobs loss.

I see the reasoning above as flawed though: if automation lowers the prices of the goods (both by increasing productivity, and by reducing costs; I'm ignoring the automation industry itself) in general, this leads implicitly (in the long term) to an increase in wealth, and by extension (again, in the long term), to an increase of the jobs offer.

In practical terms, if producing, say cars, would cost less, people would save money and spend it through other markets, say going (more) to theater; the increase of demand in other markets would create new jobs, in this case, theater companies.

I see the net of all of this as positive. Am I missing some important factors?

I can see as argument (by some) that this phenomenon could/would only lead to increased profits for the "Top 1% of the evil capitalists©".
Although undesirable, this is irrelevant - such (evil©) people would certainly spend or reinvest the money, again, leading to the mentioned consequences.

It's important to note that I'm talking about long term. I'm sure that if literally tomorrow automation would take over millions of job, it would certainly be a disaster.
I'm also assuming a healthy economy, that is, the increase of savings/profits wouldn't stay still under the mattresses.
Short-term or long-term, Property rights and distributional issues exist, "evil capitalists" or not, and they will always result in strong scrutiny of any change.  Remember that what is "short term" for society is mid- or even long-term for individuals.

Moreover, there exists the transitional pain: whether we can optimize it downwards, and who is going to feel it.

All these cause the heated arguments and the opposing positions.

But your post starts with a strange assertion: that "almost all times" it is assumed that automation has a negative economic impact. If this was so, it seems a little strange that automation marches triumphantly for the last two hundred years, and it continues to do so. If this was so, people now must live in a much worse material situation than two hundred years ago. Is this the case?