The main two reasons are safety and convenience.
No matter how carefully your watch you will not be fast enough if the prey gets a bite opportunity. This is an animal that is fighting for its life! It is far too easy for the snake to be seriously injured, even killed if the bite connects just right.

Also you may feed mice now but as the snake matures you will need to switch to rats, which are a lot more dangerous. Or feed LOTS of mice at a time which is wasteful as parts of the prey are not digestable. And a frozen rodent can't bite YOU and go scampering away into someplace you can't reach.
It is more convenient (and less expensive) to feed frozen. You don't have to worry about come feeding day will the pet store have the appropriate prey item you need. Around here this summer there was some sort of a rat shortage and the price for live went thru the roof almost doubling. I just went to the freezer and there they were!

You can order in bulk online and save lots of money! The more you can order at a time reduces the shipping cost per item so if you can find someone else to go in with you it will be even better. If you have a number of snakes then it is well worth the time. Add to that the freezing process kills many of the parasites that the prey may be carrying.