This mostly comes down to personal preference. Think about it this way: beer can be served at room temperature or cold, but when most people (in the US) ask for a beer, they want a nice cold brew. Go to a place like Germany and their beer may be served at room temperature.
One overall benefit of storing any liquor in the freezer would be making it smoother on the way down -- it eases any burn on the throat. This can apply to just about any liquor, though some types of liquor have noticeable differences in taste when served warm vs cold. A couple that come to mind are:
- Cognac (specifically Salagnac)
- Deep Eddy Lemonade
During the Hennessy shortage of 2017, many customers at our store had to look for alternatives. Those who didn't go for Remy Martin went for Salagnac. When cold, Salagnac has a very similar taste to Hennessy. When warm however, this isn't as much the case.
Both Deep Eddy Lemonade and Fireball have stronger, sweeter flavors at room temperature. When cold, the sweetness isn't as much of a smack in the face, and with fireball the flames seem to more along the lines of a smolder.
You do not put bourbon or scotch in the freezer. Both are intended to be straight or on the rocks. It doesn't make the liquor go bad in any way, but is seen as heresy and you may be shunned by friends or family. There is a noticeable difference in the taste notes of smoke and oak, so it's best to leave these ones out.
When it comes to the bar, it just makes more sense to have the alcohol out on display. It shows the customers what they can have, multiple bartenders don't have to fight for control of the freezer, and a large portion of their sales are from mixed drinks which are served with ice anyway.