Ugh, I'm starting to think that the downsides of "patriotism" outweigh whatever benefits it might have.

Patriotism is fine, you're thinking more of Nationalism.
https://www.washingtonpost.com/opinions/nationalism-vs-patriotism/2014/02/23/9129d43a-9afc-11e3-8112-52fdf646027b_story.html?utm_term=.0fb632000bad

No, I'm aware of the difference, and I meant patriotism.

From your article:
"Patriotism is fundamental to liberty because pride in one’s nation-state, and a willingness to defend it if necessary, is the basis of national independence. Patriotism is the courage of national self-determination."

If you believe national independence and national self-determination are good things, then yes.

But it's still just another form of tribalism.

I am happy for people to defend IDEAS, but the concept that there are "French values" or "American values" seems increasingly silly to me.

There are ideas I support and ideas I oppose and the nationality of those espousing them should be irrelevant. I don't blame all Americans for Trump (especially since most of them didn't vote for him) any more than I credit all Germans for Einstein.

Again, I'm kinda playing devil's advocate here, since I'm not even really sure of my own position. I'm very proud of both my country of birth and my adopted homeland.

I just wonder if patriotism isn't something that's ultimately bad for us as a species.

Patriotism is not bad, fundamentalist patriotism as an ideology is bad.

Patriotism or its effect is really just a will to support and defend a local community that can then defend itself from external forces and organize internal infrastructure and services.

National states just happen to be strongly defined communities that can be organized fairly easily.

As with other ideologies it is important to try to not let one take over the state without any recourse.

Misuse of xenophobia in politics is just as worrying as the apparent lack of will to defend the "European community" from external forces. No one is willing to die in trenches in the name of Europe just yet. And there is still a lot of internal xenophobia within Europe.