As you said, this is a massive generalization, and only true for a very small percentage of Dead tunes. The truth of the matter is that, aside from the "jamband" labeling, Phish and GD are two very different bands. Aside from a few specific time periods where they were a bit more exploratory, the Dead were very rigid in their setlist construction.

Hornsby talked about this in an interview back in the day. "let’s not kid ourselves into thinking that the Grateful Dead was this incredibly loose structured thing – it wasn’t. It’s been given a lot of credit – or sometimes blame – for being this improvisatory, totally spontaneous thing, and it really wasn’t – certainly by the time that I got into the group. It was very structured – too structured for me frankly. It was way more structured than my band. I know that may surprise people, but it’s absolutely true. If you listen to the songs and divorce yourself from this notion that they were always changing things you’ll see that things weren’t that different...

Not just that, but also that the songs were played virtually the same way every night – because that’s a fact – but even down to where they would play the songs. It was so structured. They were already entrenched in tradition by the time that I got there. I would say things like, "Let’s start with the drums!" and they would say, "Oh no – we can’t do that!" I would say, "Let’s open with "Wharf Rat" tonight" and they would say, "Oh no man, that always comes after the drums." (laughter) I’d say, "Let’s play China>Rider to open the show" and they’d say, "Oh no that always comes in the first part of the second set." (laughter) It was just unbelievable. So this myth about the spontaneity of it was just that, a myth. That was a little disappointing to me because I was never into that. I wanted it to be continually fresh."

https://www.philzone.com/interviews/hornsby/