Lost my first reply (cell phone).
There is nothing wrong with putting machines on wheels for mobility, i would not hoever suggest running the while on those wheels.
There are two problems with wheels and machine operation. The first is that floors arent flat and router frames are not perfectly stiff. This means that the frame will twist to conform to the floor or try too. A twisted frame is bad but you can manage that with simple leveling feet. For example:
Leveling Devices (ANSI & Metric) | Vlier Leveling Devices. The second problem is machine walking during operation that is when you buy feet with rubber pads.
I linked to the Vlier site but i need to say i don't like those types of feet on machines of any size as the studs are easy to bend. There are other types of feet that are somewhat more resistant to bending and you can even get leveling castors big enough for the job. Unfortunately looking for examples crashed my phones browser so no links at the moment.
Leveling your machine after a move is very important in my mind as an induced twist will show up in your work. Obviously machine size here is a factor, as is machine stiffness but you are far better off with a leveled machine before putting it into production. Some people can get away with a twisted machine but i don't see you doing that while trying to turn a router into a mold making machine. By the way we are talking precision leveling here.
So wheels are good and even better if the frame is designed from the ground up to support the wheels and the jack screws to stabilize it. You might be aware but there are a number of sub frames sold for wood working machinery to supply the machines with castors. Some of these are excellent but many are flimsy and frankly a safety issue. Designing in your own solution should make the castors mechanically strong to the frame. So that isnt an issue. The next problem is one of stability which requires more thought. A machine on wheels can be subject to tipping forces not seen in a stationary machine so you really want to consider machine stability when rolled around. For most routers this probably isn't a huge problem but might be on a long narrow machine. A floor standing drill press on wheels is an extreme example of a top heavy machine that could easily roll over during a move. I only mention this due to having to repair rolled over machines, machines that where top heavy and relatively narrow.