Is there such service that could transfer money from user's PayPal account dirctly to my bank account even if I don't have a PayPal account?
No, this is not possible. PayPal only supports:
- transfers between two PayPal accounts, and
- transfers between a PayPal account and its associated bank accounts or cards.
This makes PayPal unsuitable as a general payment method or as a general-purpose bank account.
To transfer money to a recipient who doesn't want to open a PayPal account, you will need to use a different method. If the money you want to send is on the PayPal account, you will first have to withdraw it to your own bank account.
I too would love being able to transfer money without having to withdraw it first, because a direct transfer would circumvent PayPal's exorbitant currency conversion fees.