I bank at Suntrust as well -- if I'm banking, I will park in one of their reserved spots. If not, I don't. Have generally not found it to be a problem when I've needed to stop by there during the day. And, as a practical matter, these things are terribly difficult to enforce. Someone could park there, legitimately run another errand or grab coffee, etc. -- and does the bank really want to mistakenly boot a real customer for an infraction. I don't think there's gonna be a huge desire to do that.
Then your concern is just inapplicable after-hours.
Ultimately though, if the owner wants to enforce tenant reserved parking, if properly noticed, they have a right to do so. But it's definitely very anti-community and would have a negative impact on surrounding businesses.
Presumably the tenants could have some voice re: enforcement on the lot tied to the building. The other parcel (and I don't believe it's signed in any fashion -- and, doesn't it also contain the Suntrust drive-through -- might be more open game for a new owner trying to maximize the asset; ST might have a relationship, but not sure how much of an ally they would be unless forced to do so. I would doubt any space there is dedicated for the drive-through. So, it could be closed off and parking prohibited, while the owner tries to find someone in EAV who will lease the lot -- same situation as with the adjacent Earthshaking Music lot.