As a bartender and bar manager for 10+ years at a very busy bar several reasons are obvious to me.
Not everyone wants a cold drink. It is easy to chill warm liquor quickly. On the other hand there is no readily available method to warm chilled liquor.
As for having a copy of each liquor on display/ room temperature, logistically and financially it's infeasible for most bars/ restaurant and massively inefficient for larger establishments or commercial chains.
In your mind's eye picture how many bottles you might see on display, then picture how much space you need to store them. Another problem becomes apparent. On display there may be 30-100 bottles of liquor lined up in a way that their labels are visible.
This does not maximize storage space, but having the label visible serves two primary purposes:
1. Customers can easily see what's available and
2. Perhaps more importantly, especially for busy bars, the bartender can quickly find and grab a bottle when needed.
If the bottles are stored in fridges, either top or front open, they will need to be stored one in the front of the other to best fill the space.
An important axiom in restaurants is that your peak business is constrained by how many customers you can serve at once. Having to open doors every time you wish to pour a drink is a massive time sink. Perhaps if only 1 or 2 drinks were made every 10 minutes then it would be trivial, but if bartender needs to make 3+ drinks a minute(and a good owner will build to support busy times), or if 3 or more bartenders need to do this, then the 4-30 seconds seconds it takes to open the door find the the bottle, and/or clear bar path obstructions this causes add up to massive increases in wait time.
Moderately Busy bar with well-skilled bartenders scenario:
4 bartenders making 3 drinks each per minute = ~12 customers served per minute.
Goal- guests greeted in 30 seconds, drinks delivered with a minute of greet time. Why? This is roughly the time window for someone to feel they got great bar service. This is a widely upheld service standard.
Each drink takes 20 seconds to make. Add 4 seconds to each drink and also assume that sometimes there will be wait at the door to get the correct liquor, or the open door is blocking the path.
Possible cost of having a door: the door can add (3 drinks x 4 seconds)x 3 bartenders = 36 seconds every minute to each bartender. More than a 50% increase to serve 12 customers. The service standard can not be met and the number of people served per minute with the same staff falls considerably to ~7 (12/96=.125 guests per second *60 seconds = 7.5 guests per minute)
This could problem could be mitigated by increasing the size of the bar to hold shallow, but long refrigerators that have sliding doors and allow for alcohol to be seen and easily grabbed. However, this does not solve the problem of people who don't want ice and it costs a considerable amount more in square footage, and refrigeration cost.
And of course all of these concerns are easily answerable with using scooped ice versus refrigerators. Scooped ice is elegant, refrigerating all the bottles is a kluge.
Good logistics and bar design do a lot of work towards serving customers in a bar and towards reaching profitability. With elite logistics you only need average bartenders to create excellent service. Add elite bartenders to elite logistics and you create world-class service. On the other hand poor logistics can make elite bartenders seem only average and make average bartenders nearly worthless.
One last thing: Adding ice adds to perceived value with very little relative cost. The glass size can be doubled and still be filled with the same amount of liquor. While in truth you are getting the same volume of alcohol and/or mixer it appears like you are getting more add the cost of a penny or less for the ice.