Why do computer science conferences (usually) not reveal the number of submissions? In the conferences I've experienced, each paper gets a serial number that can tell its authors how many submissions were made prior to theirs.

Many conferences have a fixed number of tracks (and days), and thus the number of accepted papers cannot vary too much. (The organizers do have some flexibility, but it is rather limited.)

Thus, knowing the number of submissions can help one assess his chance of being accepted to the conference, which might tempt him to submit at the very last moment just to figure out the submission count.

Obviously, not everyone can do this. Why don't the organizers simply post it on the website after the submission date is due?
Usually (most of the time) this information is shared on the opening day as part of the welcoming session. 

Why do conferences use sequential numbers that could give this sort of information away? I don't know, probably because it is easy, and the information has little value in general. Since most of the review process is a pretty manual labour intensive task, this probably makes it easier to find missing papers by hand, to search for and track papers, reduce potential administrative errors, etc.

What would change if there are 300 spots and your paper was number 600 vs 350 (assuming you submitted last)? You are usually not allowed to submit the same paper to more than one conference at the same time, so you cannot act in either case until you received your acceptance/rejection letter. Good conferences cull poor quality papers, even if that means not all the spots are filled. You only know the paper is accepted when it is accepted. Estimating a probability of acceptance is merely for your own enjoyment and has no benefit to the conference organisers. 

In academia, if you ask the question why is x, y or z not done, the answer is usually time and effort required without any benefit to that person.