Why are bicycles triangulated at the back but not at the front? I know that triangulation of structures makes them stiff. Why are bicycles stiff at the back but not at the front?
Forks on bikes and motorcycles do pay either a weight or stiffness/strength penalty for their lack of triangulation. One can imagine systems for steering the front hub with a linkage rather than a conventional cantilevered fork. That sounds more heavy and complex than it's worth for a bicycle once you have it able to handle the full range of motion needed, but that's just a guess, and it's not say there's not some other application for such an idea.

One piece of the answer is that the main drawback to a cantilevered fork is that they're vulnerable to being smashed into things head-on. If all else was equal that would be a nice vulnerability to eliminate, but it's hard to imagine a situation where all else is equal, especially considering the forces the bike encounters in such incidents are quite high. Good forks offer a degree of valuable micro suspension even if they're not suspension forks, and losing that just to be able to smash into things would not be a welcome compromise for most.

This is to say that a more triangulated design employed in a way that increases stiffness likely would be unwanted. If you could keep it at the same stiffness but with less weight, I would say the main reason that doesn't exist is no one's been able to figure out how.