Running shoes, yes they have good cushioning, yes they are light weight, yes they are breathable.
Those sound like good features you'd want in a shoe to play racket sports.
But, unfortunately that's not totally true.
Court shoes use less mesh and are less breathable so that they can be more durable and supportive when executing lateral movements.
Court shoes also use specially designed gum rubber soles to provide maximum traction, and not all court shoes are equal in this regard.
Good court shoes use a specially designed cushioning system that provides excellent cushioning, and also allow you to be more agile than in running shoes.
Yes, court shoes can also be light, but there has to be a balance. If the shoe is too light, you'll be missing out on either extra cushioning, or support that your shoe could have had.