This thread has popped up so many times. The short answer is yes, some people cross the US/Canada border undocumented and get away with it. Other people attempt to cross and get busted. A few attempt to cross in the backcountry and die because they aren't prepared to hike the backcountry. Look at a map, consider your options.
The thing is, for most people, getting a US passport is a small cost in exchange for the huge privilege of being able to travel freely not just across one border but almost 200 other ones for the next 10 years. If you don't have extenuating circumstances that prevent it, a passport from a country like the US is one of the best things a traveler can have in their back pocket, because it unlocks a literal world of opportunities. That is why people recommend it as the first choice.
Canada is a nice place to visit and a nice place to live, but if you really plan on emigrating and not just swinging through to bum around for a while, that's even more reason to get your paperwork in order. Immigration is a massive, bureaucratic pain in the ass, and there are no short cuts. Even arriving as an asylum seeker involves a lot of paperwork and legal wrangling. Remaining undocumented for long periods only really works if you don't mind always living under the radar. If you're trying to escape legal problems then maybe going overseas where you risk more legal problems will only add to the anxiety? I don't know, maybe not. Good luck to you either way.