This is the one piece of gear advice worth taking seriously, and it is the mistake almost every new player makes — including turning up in perfectly good, expensive running shoes.
Running shoes are built to move you forward. They have a raised, cushioned heel, a soft flexible sole, and a narrow platform, because running is a repetitive forward motion. Pickleball is not. Pickleball is short, sharp, sideways — split-step, lunge to the kitchen, push off hard in the other direction.
On a lateral push, a running shoe does two things you do not want. The soft sole rolls, taking your ankle with it. And the outsole — designed to grip going forward — skids sideways on a smooth court surface.
Court shoes are built the opposite way: a flatter, wider platform, a stiffer sidewall that resists rolling, and a herringbone or modified-herringbone outsole that grips in every direction rather than one.
There is also a boring reason clubs care: court shoes are non-marking. Many indoor venues will turn you away in street or running shoes because of the scuffs.