I think it is state bank policy for USD to keep it out of any sort of online banking. SCB does the same i.e, you cannot transfer or use dollars online. You have two options, go to bank and deposit USD to your PKR account (inter bank rate will be used for conversion ) OR you can go bank, withdraw USD in cash, get it exchanged in open market and deposit in PKR account. You cannot have debit card even for USD account.
Moreover now a days, gov has made it very complicated to open a USD account in order to discourage it. There are plenty of forms and proof of income and tax required now to open USD account (happened with my one colleague recently) unless you have good terms with Bank Manager and only then he can bypass some of the formalities.
My suggestion: stay with your bank for USD account and get used to it 