FWIW, we have two Toto 1525 cast iron tubs with no-slip grips on the bottom, as well as a Kohler cast iron shower pan with no-slip on the bottom as well. Ours look as clean and white as the day we got them, and they really aren't difficult to clean.
Every week to two weeks I clean-clean the tubs (we wipe ours out with a paper towel after showering to get rid of loose hair, or errant blobs of shaving cream, or conditioner). I spray with Lysol aerosol bathroom spray, let sit (for however long it takes me to clean the sink, toilet, tub surround), re-spray if needed, and then clean it off with hot water from the tub filler faucet, and a wet microfiber cloth. That's it.
If the no-slip grips do happen to look grimy (very dirty bare feet will sometimes leave smudges, as will the bottoms of rubber soled work boots worn by someone working on the plumbing or tile), I will take a Mr. Clean Magic Eraser, dampen it, and go over the floor of the tub with it (usually a light rub is all it needs, occasionally it takes a slightly stronger touch).
To address the height/stepping into the tub "issue", you can have the tub "recessed" into your floor. Our plumber told DH to use thicker plywood for the second layer of sub-flooring, after the tub went in, so the sub-floor under the tub ended up being a little lower than the floor surrounding the tub when all was said and done. This way, the step into/out of the tub is easier.
HTH!
Q
Shower
Q