I mean, they sort of did, right? Or at least, there was a lottery element to the sign-up process.
For those who entered the pre-queue before 10 AM Eastern, they assigned a spot in the queue randomly. So regardless of your browser or internet connection, once they had your details your place in the queue was assigned by lottery. (After 10AM, new entrants were assigned to the back of the queue.)
Now, that's not a true lottery, as the randomization only impacted those who were on top of it enough to be in the pre-queue holding room. If they shifted to a true lottery, you could have a much larger number of aspirants entering the lottery over a period of weeks (I'm thinking of my friends who tried to sign up a few months before, and were surprised to see it was already sold out). That would hurt the chances of those of us who are more aggressive about signing up.
Overall, I think the semi-randomization is nice, in that it levels the playing field for those of us who are really on top of it, especially those worried about wi-fi connections or browser types, while still avoiding the pitfalls and loss-of-control that comes with a full lottery system.
More capacity would definitely help more folks get in, though!