A couple of things. First, though it's been pooh-poohed on this message board before, it's very important to keep your population as high as possible. That means keeping taxes quite low for a long time and researching farming techs up to the max. A planet might have 50% approval, but if it's also got 30 billion people, it's practically invincible. There are ways to keep planets from ever rebelling, no matter what the approval rate. I've had planets at 50 billion people at 10% approval for a couple of months, and it's been fine.
Second, the soldiering bonus is wonderful. I play a custom race, which gets 20% soldiering at the start, and then I research all techs that increase the soldiering bonus. When you invade another planet with that advantage, you can have 3 billion take out 11 billion easily. You'll notice that your enemies can't do that, even though you're disappointed that the bonus doesn't always work as you'd expected. In my current game, I've had the Torians, with a far superior military, invading my planets for months now. They haven't taken one yet. My population is always high, and the huge soldiering bonuses, though not giving me the ultimate advantage when invaded, have given me enough that they just can't get over the hump to take a planet. So, I'm surviving in an environment in which the Torians totally control the space around all my planets (huge galaxy). That's just from pop and soldiering. In other words, don't take it lightly. Sure, I'd love to control space, but since I've just fought a terrible war to wipe out the Yor, I have to fall back entirely on defenses at this point. If I didn't have the pop and soldiering bonuses, this game would have been over long ago.
I'd love to hear comments from those who have different strategies on this. However, those who say, "Don't let a planet get over 20 billion pop," or whatever their number is, probably haven't had to deal with this kind of total domination from an opponent's military. Sometimes it's only population that will save you, and that you will eventually parlay into outstanding invasion forces.