Can double-spending be prevented by imposing rules for initiating new transactions:
RULE1: Account can only initiate 1 transaction every 60 sec
RULE2: Account cannot initiate new transaction before previous transaction is validated.
First of all, Bitcoin doesn't have 'accounts'. There are private keys and their associated public keys and addresses. But lets assume you meant those.
What is stopping someone from simultaneously broadcasting transaction A to nodes 1, 2 and 3 and transaction B, which tries to spend the same coins as A, to nodes 4, 5 and 6? Both transactions are perfectly valid when seen by the nodes that they were broadcast to and only when the transactions propagate through the network will some nodes receive both A and B, in which case they simply drop one of the two. Nothing in the rules you propose prevents this.
Adding such rules to the users client-software is pointless (and current clients already try and prevent doublespending), since a malicious user may as well develop his own version of the software that doesn't include these rules.
As DannyHamilton has pointed out, doublespending is already prevented by design. In fact, this is one of the more important innovations of Bitcoin: a decentralized system with doublespend prevention. However, the caveat is that some time is required before a recipient can be confident that a transaction will make it into the permanent ledger.