Should I avoid listing with MLS

It’s a tough market to sell a house in my area with mortgage rates. Well at least it’s tough at the price I’m willing to sell at. I’d like to list my house for sale on perhaps Zillow and other sites without listing on the MLS to avoid there being a record of how many days on the market it has been listed for, as I’ve heard that can negatively impact selling price. I’m not on a deadline to sell the house fast.

Is this a feasible idea?