Interestingly, I too thought that palm trees looked “trimmed” because the dead fronds just fell off. Not always true, however.
On a quick trip to Palm Springs, we drove out into the San Andreas fault canyons (the actual physical fault, geologically very interesting). There are very old palm trees out there that have never been trimmed, so they actually resemble a thatched hut, very fat with old fronds still attached going all the way down to the ground.
But maybe that’s only one type of palm.
The palms in our yard get trimmed (especially when they are dropping fruit), and you can also “shave” the trunks for a clean look.
With Washingtonia (both species, the one out in the desert near Palm Springs being W. Filifera), frond retention can be variable. In more humid climated they degenerate a lot quicker and fall off faster. I’ve noticed the taller they get the less inclined they are to keep them, although i have seen them with dead fronds all the way to the ground. Sometimes vandals will set the thatch on fire, which doesn’t usually kill the palm. They can be kept trimmed, or the old leaf bases (called “boots” in the palm world) can be pulled off.