I was a robotics software engineer on a project that built a mecanum wheeled robot. The big problem is that the rollers are small relative to the wheel. You know how bicycles handle rough terrain better than skateboards? The actual rollers on a mecanum wheel are pretty small compared to the diameter of the wheel they are mounted on. Our robot could handily carry a person on a flat floor (the engineers mounted a chair on a prototype and we got to sit on it and drive it with an Xbox controller - an actually extremely fun activity that could make a nice carnival ride). But if the robot encountered a pencil on the ground, the rollers couldn’t roll properly and things would get messed up.

I think I’ve seen suggestions of using the wheels for mars rovers, but a mecanum wheel that works in sand would need the rollers to be very large, so the actual wheel would be huge. That would suck up all your weight budget for your robot. Ackermann steering is lighter.

All that said, when you have a controlled environment with a flat floor, mecanum wheels are pretty rad!