Persistence allows the scammer free license to attempt password recoveries for every account the victim could possibly have. Other banks, retirement accounts, the victim's email account.
Scammer that thrive are greedy, but not too greedy. Easier to break into one type of account for 10 victims, than to break into 10 different account of one victim. Persistence is risk.
When the victim's relatives send them money because they need to eat and pay rent after handing everything over to the scammer, the persistent backdoor lets that money be drained as well... You're underestimating the persistence and ruthlessness of the scammers.