Which do you perfer? An identity created by Bruce or a costume to be pass down to one man to another? Do you want Batman to be immortalized or be worn by only Bruce?
One problem I have with the costume being passed down to different guys is that some guy 1000 years from now could use the Batman persona for evil purposes like revenge or to commit murders. That would hurt the Batman legacy. Bruce can't be sure the future Batmen would be all good guys.