The cost:benefit of colonizing the new world was immense and known prior to widespread colonization, esp. in the tropical parts.

Settling mars is like colonizing the Sahara desert, except this time with no oxygen or camels.

I'm not sure which exact path for advancing humanity into space is the best. Perhaps there are better ways than colonizing Mars.

However, in general, there are immense resources and energy sources in space that can benefit humanity. Pioneering space will also require many technological advancements that will benefit people back on Earth.

There is also the question of learning about the universe. If, for example, there was bacteria on Mars, that would one of the greatest discoveries of all time.

I don't think your comparison is fair.

They are far higher now. See Asteroid mining.

Would traveling across water to open new trade route to make more money, and just happening to stumble across fertile, richly-resourced new territory... be even a remotely good comparison to make with traveling across space for years, getting irradiated, landing on an inhospitable planet with no breathable air, nearly constant cold temperature, no timely resupply or assistance, and essentially no hope of return to home planet either for humans or for any valuable mined resources?

The value proposition just isn't there for colonization of Mars. If you want to say you did it for bragging rights, then just say it. Anything else is foolishness.

They weren't just going across the Atlantic just because. They were looking for a new trade route with Asia. Discovering the New World was just a fluke.