I think it would make for a very strange looking plane.  I use the eFlight light wheels, but no bigger than about 30mm ('cuz that's what looks good).

If they still make roll-up bamboo blinds, I remember one of those working very well as something that can be laid over grass for a take-off space, and rolled to a very compact bundle when you're not flying.  Then you can use little wheels.

I guess it depends on the bumpy spots.  Can you scuff them smooth, or bring a garden rake (which you keep in your capacious trailer) to rake them out?

It could be an interesting idea. Kind of like the new bush planes that Husky and Cub Crafter build.

It wouldn't render the plane unflyable unless it was already there -- but it would certainly add a lot of weight and drag.

I've used the wheels that come with black hawk models and skinnier smaller ones that eons ago came with Carl Goldberg models on dirt many times with no problems - on take off at least.  Until I moved a couple of years ago I was flying 1/2a on a soft ball diamond near my house.  I used the line between home and first base for a runway but I would back up so that I landed in the grass when the fuel ran out.