* Although you can make the enveloping sphere as large as you want, the (anti-)equilibration process requires a sphere of some finite radius because if you wait long enough a few stars eventually get launched at escape velocity, and if these actually escaped they would effectively cool the remaining stars.
* Therefore, the characteristic time scale for this process (i.e., the timescale on which the average kinetic energy rises substantially) gets longer and longer as the sphere gets larger.
* In order for the pressure and average speed of the stars to keep rising, the gravitational potential needs to keep falling, so at least some stars need to get and stay very close. In real life, these turn into black holes, which cuts off the process by limiting the amount of gravitational potential energy that can be unlocked in any given volume with a given mass.