There were several good reasons for Alexander wanting to have the bridge, and thus let his men chase after the fleeing enemy.
One was because his officers were right. Killing even one of them would reduce their opponents by that amount.
And even if the size of the garrison seemed inconsequential, a few hundred at best, well even if only a drop of water from an entire ocean was lost, that would still count as being lost, no matter how small.
And Lord Parker's forces were certainly not as vast as the oceans, amounting to only twenty thousand.
Two was because he felt this would be a good way for his men to vent all their built up frustration, and to get some of the rust in their joints out.
Because in recent days, Alexander had been getting worried that the men had been cooped up in their tents for too long, only having themselves to dig new wells and drink melted snow while killing the rest of the time in wasteful sloth.