The UNO predates the Pi Pico by about 20 years. It was pretty small for everything it did back then. The headers are laid out in a standard format so that it can accept "shields", so now anything that wants to use those shields has to be this size.
The first Arduinos with that formfactor which supports shields are from around 2005[0]. The Uno wasn't the first[1], it was just a model line set up for that specific formfactor for consistency, since the name was changing frequently (e.g. "Arduino Diecimila", "Arduino Duemilanove", etc).
If you're not interested in shields, I don't think there's any reason to use any type of Arduino today. There are smaller Arduino boards that don't support the same shields for people that want something smaller. But, today, the ESP* boards are way, way better. And, as you mentioned, some of them have shields too (though not anywhere near as many as the UNO).
I like the feather format a lot as well and Arduino makes some in that shape (and smaller) but having taught a number of beginner's classes with Arduinos at my hackerspace, I think the Uno format is a bit friendlier for novices. Having a wifi/bluetooth enabled board in that shape is great.
It's easier to see what you're doing and plug a rats next of wires into the bigger board without it falling over, and everyone's got to start somewhere! Uno format Arduinos are a learning tool first and foremost and they do that job really well.
According to [1], the decision to keep the spacing for compatibility reasons was a conscious one. I can see how they might want to keep the whole ecosystem of Arduino-compatible accessories/kits/etc functioning.
