You don't even need iron wombs. The thing about the Clans is that you can artificially set your population numbers at whatever you want, and justify it pretty easily. 300 years is enough time, particularly with a crazy dystopian social structure, that you could have massive population growth without a problem.
In real life, more technology and higher standards of living tend to lower birth rates. You can afford to live in a bigger house and buy that 80" TV when you aren't paying for a bunch of kids. Women tend to delay having kids, and have fewer kids, when they have more education and job opportunities. But... that may well be situation specific to our modern societies. Change a few factors, and everything could be different.
In the Stephen King book The Stand, a super-plague wipes out 99% of the people on Earth. Everybody is gone, but all of our stuff is still laying around, just waiting for somebody to come along and use it. In a situation like that, if you want to increase your standard of living, you need to
breed. You need a larger population so you can have people to operate the machines. You need oil field workers, you need people trained in repairing old equipment, you need manpower. Your standard of living will skyrocket once you get the old stuff back online.
The Clans are kind of in a similar situation. They arrive on uninhabited worlds, the first thing they need to do is grow their population so they can establish industry. They don't have a planet's worth of equipment laying around, but they did bring a lot of technology with them and they understand how to produce more. The Clans have a culture that places extreme value on being useful to the group, and very little value on your personal desires (unless you're a warrior). There's a big advantage to the Clan in having a large population. You think they wouldn't tell labor caste women that their job was to pop out kids? Your kid will probably be raised in some big group home anyway, so it's not like you even have to raise them yourself.
Right now, Africa's population is projected to grow at 2.3% a year until 2050. That's just natural, not some oppressive space government trying to force higher growth. I've been playing with a population growth calculator (
http://www.metamorphosisalpha.com/ias/population.php ). At 2.3% for 300 years, the 6 million people the SLDF took to the Clan Homeworlds would become 5.5 billion. Bump it up to 2.5% for 300 years, and you get almost 9.8 billion. At 3% growth, it's 42 billion. At 4% growth, it's 773 billion. At 5%... you get a population of 13 trillion people.
You think the Clans can't grow faster on purpose than Africa is doing by accident?
