You are losing out on at least 600 cash just for the crystals. Most likely you'll be paying more, since crystal starts at 400 and drops, unless other people are buying crystal, in which case the price skyrockets. So let's say 700, for two buys of Crystal at 350 each, since that's about what I got when I tested with TEC in single-player.
Okay, so you're down 700 cash, but at least you've got 200 crystal.
Now you build that population cap increase, which costs another 750 cash and 225 each of metal and crystal.
It's maybe 5 seconds into the game and you're already down 1450 cash, 225 metal, and 225 crystal.
What do you get out of this, exactly? Well, (again, testing with TEC) your population cap goes from 190 to 280. At the population growth of .1/sec, this takes 900 seconds to fill up, or 15 minutes. You begin at 11.x cash/sec and end up with 14.1 cash/sec. So you've got an increase of 3 cash/sec. 1450/3 = 483.3 seconds, or 8 minutes. It takes you over 20 minutes to break even.
How is this, in any way, worth it? You are losing out on resources that could've gone towards necessary planetary improvements for newly conquered planets, resources that could've gone towards ships to help you clear planets faster and kill the other player. The beginning of the game is a very important time, and you don't have resources to burn like you do later on, especially once you get your economy off the ground. Throwing away money to something that takes 20 minutes to break even, to even start being profitable, simply does not make strategical sense.