I’m not much of a military expert, but I do know a little and I can see a couple of reasons why Vercingetorix allowed himself to be “pinned inside a bottle” at Alesia.

First of all, if memory, serves he had just suffered a defeat. Now, even if he had retired from the field of battle in good order, a defeat meant that he needed to regroup and reorganize. He couldn’t do that on the run with Caesar harassing his flanks and rear and generally making life miserable. That meant that he needed a fortified position such as Alesia. He could only hope that he would have enough time to do what needed doing before Caesar arrived and laid siege.

Secondly, moving into Alesia was a way of dictating the field and making it as much in the Gauls’ favor as possible. This has always been the function of fortified positions. They keep an invading force from roaming completely at will. They must pay attention to this armed position of face sudden attack from an unfavorable quarter at an inopportune time. Tied to this is the fact that Vercingetorix had another army out there. 300,000 men is probably an overstatement, but even a tenth of that would be the equivalent of 5 legions and puts Caesar in a bad position. The besiegers suddenly became the besieged, caught between two forces. If the Gauls had been on a more equal footing with the Romans in terms of discipline, tactics and equipment, Caesar would have been very hard put to get out of there alive.