But you would also need a lot of cargo to support those people. In fact, your cargo to person ratio is going to be quite high. It would probably be 10 cargo trips for every human trip, so more like 100,000 trips. And we're talking 100,000 trips of a giant spaceship.
And what is the cost, both in terms of resources and pollution, of launching 100,000 times? Even if you kept it in orbit and brought people up to it it's a huge cost.
Perhaps the cargo transport can be done cheaply, without rockets or heat shields: a rail gun in earth orbit, loaded from a space elevator, and a reverse rail gun channel around Mars to slow them down, with another elevator. Just some thrusters for alignment fine tuning.
I think the romantic idea of space colonization is pretty cool. But I don't really think it's quite as viable as people like to think it is. At least not with current energy requirements and sources.
Outside the Earth, the solar system is a pretty boring vacuum with a bit of gas and dust. But the insurance policy argument is pretty compelling, and the engineering project would be an exciting way to encourage all nations to work together.