I have a very small shop. I wanted to put my drill press in the shop. I did not want to take up space on my workbench
and I didn't want to stuff it in the corner where the walls would get in the way when I worked on larger pieces. The solution was a cart, but there is a reason why drill presses are not sold with wheels on them.
A drill presses is very top heavy. It needs a stable base. If the floor is not completely flat, it is fairly easy for the center of gravity (cg) to shift outside of the area enclosed by lines connecting the contact points between the base and the floor while moving the base. When that happens, the drill press tips. Even if the cg doesn't cross the line, a drill press being moved on wheels has momentum. When a wheel hits an obstacle, the bottom of the cart stops moving, but the momentum continues to push the cg. Because the cg is high, there is a lot of mechanical advantage so even a little momentum can cause a tip.
The solution is to space the contact points as far apart as possible and to lower the cg as much as possible. There is a limit to how wide and deep you can make a drill press base since you need to be able to easily reach the press handle. Likewise, there is a limit to how low you can Lower the heaviest part of the press.