We ask for a payment method when someone starts a free trial to verify there is a real person behind the account. This also prevents people using multiple Chess.com accounts to get free premium benefits over and over again.
Also, please remember...
If you cancel the free trial before it ends, you aren't charged anything.
If you forget to cancel in that time-frame, there is still a full money-back guarantee for 30 days for first time buyers. This provides lots of time (risk-free) to decide if premium membership is right for you.
Even if you try the Trial, don't buy membership, then months later decide to buy premium, you will still be a 'first time buyer' and have the 30 day money back guarantee!
Give it a try!