Abolishing tips isn't necessary to do this, all you have to do is set prices appropriately and pay the back of house staff correctly. (You know how some restaurants add a front-of-house "service fee" on large groups in lieu of free tipping, just do the same thing, except roll it in before computing prices, and that's your back-of-house volume-of-service pay. If you don't want to have it be a volume-based, on-top-of-hourly wage thing, do the same thing to calculate prices, but project your average volume and set your hourly wages appropriately to include what your existing wages would be plus the average amount the price increase would provide.)
It does mean that your price will have to be higher relative to your food cost than other restaurants, which might lose business. But if retaining cooking staff is valuable enough that you want to balance things, this should actually pay for itself. And, anyway, getting rid of tips and rebalancing pay between front of house and back of house means either you are going to lose front of house staff to other jobs more easily (because their total pay is cut) or increase prices just as much as you would without abolishing tips to boost back of house pay plus enough to replace the tips. Abolishing tips has no real effect here.
But by replacing tips with a 20% cost increase means the customer stays at the same cost to them.
It is against the law to payout the kitchen staff from the tip pool so the front of house tend to make lots more money than the kitchen, making it harder for them to find kitchen staff.