If you are talking about not using the anti-slip/fatigue mats…I am not sure anyone makes a flooring that does the same in a high-mess environment. We use them in our plant around the steam kettles and yes they are a mess and a pain…but needed. Sorry not much help. I did have a thought. A number of years ago I remember a rep that came in with slip covers that went over workers shoes that were both anti-slip and helped against fatigue. With us being a large facility and already having all the other coverings… prep coats, gloves, hats, face shields… we thought that adding shoe booties to 200 plant workers was an additional headache. Not too mention having to wash your hands after you touch your booties…but might work in a smaller kitchen with less mess and people. I did a quick search and did not find anything…maybe never took off anywhere. Best of luck too ya.
Just a side note on flooring, and I know not applicable to this but just a tidbit. A friend of mine that does outsourced assembly work for companies installed the same material that they use on college running tracks. It is a Goodyear product made of shreaded tire rubber. Gives good anti-slip and lots of cushion for workers standing all day without the use of fatigue mats. Just not ideal for wet or high-mess areas that need washed or mopped down daily. It would be nice if someone came up with an applied product or permanently installed tile that would both save the stress on the employee and be washable. Dare to dream!