There are mining colonies, prison colonies in harsh habitats, cultural experimental colonies, religious colonies, etc. But for any of them to last or prosper, they had to be economically feasible. And the most successful had all the resources necessary for survival in situ. Obviously, in the modern world we've grown tremendously interdependent, but a colony wouldn't necessarily have to be nearly so interdependent. There is certainly precedent to have occasional supply ship of high tech items come at considerable expense to resupply a mostly self sufficient colony (East Coast New England colonies for quite some time). At first many of these operated at a loss or barely break even, but there was promise of profit.

I agree the key to accelerating the ability to profit in space is reducing the cost to orbit. My own expectation is that it will take something like a space elevator breathrough to truly bring about rapid colonization. Even without that it could happen over a long period of time. I believe eventually we will prospect a number of asteroids and one of them is going to be loaded with usable resources, that we can exploit relatively cheaply. Autonomous intelligent probes using gravitational highways will be able to move cheaply among space pathways to and fro asteroids.

If enough of Mars is prospected, everything needed for subsidence living may be found there. If enough is found within a reasonable radius a seed colony might well be viable. I wouldn't expect much growth like bacteria in a harsh environment, but just returning knowledge could well support a small colony to pay for occasional hi tech resupply.

Using some amount of govt funds for exploration and search for knowledge is fine and there is a lot of precedent for it. When it gets down to colonization, unless it is economically sound it is doomed to failure. The example railroad and interstate highways was not funding colonization, but transportation between already viable colonies. It would be interesting to have an alternate history without subsidizing the railroads. I think without a doubt they would've been created anyway, possibly without the absolute power wielded by the robber barrons with govt backing.

Incan gold, tobacco, furs, corn, wheat, buffalo, timber, arable land, etc, are what paved the way for colonization of the new world. The govt funded some initial exploration, but then many private companies (e.g. Hudson ) funded follow on exploration in order to give shareholders good return on investment by finding resources to exploit.

In the far future, I certainly see large scale colonization. I would expect self replicating, self repairing machines to exploit vast resources on moons and asteroids, and ultimately build vast habitats (e.g. dyson swarm) for human habitation. Possibly hundreds of space elevators would be in use on earth and through out the solar system. Solar power would be utilized on a massive scale once again with structures built by an automated process.