First there is a rule, by International Padel Federation:
>"Players will wear suitable sports clothing and footwear. Swim wear is not allowed. Failure to comply will result in a fault being given. If not rectified the player will be disqualified"
Second, there is your own security, artificial grass is not very friendly to our feet and the kind of movements we do in padel. It's also a way to protect your feet from heavy impact and contacts (with your partner, balls, rackets etc...)
Third, hygiene and health.