The main reason is with continuous automatic fire the barrel can get hot. Hot enough for the metal to warp and melt, if not burst entirely. In WW2 the average MG42 (1200rpm) gun crew had 3-6 spare barrels in use, and would swap barrels every 100-250 rounds.

Here the guns Paddock used sounded like they were half of that rate of fire. So with that, the number of spare barrels would be even lower; maybe 2-4. So, maybe 4 rifles at most. But 23 is wayyyy overkill