I will probably be in the minority here.
My opinions.
Depending on the type of ad and why a member was banned would play heavy on the decision to delete. Also, many banned members aren't banned indefinitely. So a blanket delete all ban members ads wouldn't be feasible. Also not really helpful to those that are in current transactions with the person.
Really depends on if the person is a obvious overseas scammer or a member that was banned for a rules violation.
Bandwidth wouldn't necessarily be saved because we might still store them just not in public view.
My thoughts differ for one main reason. I believe it is almost always important to have more information than less.
As with your example,
Apparently, having a Mod point out that a seller is banned and has used stolen pictures just isn't enough to dissuade some people from pursuing a transaction.
Even with a moderator stating the user has been banned, that the name or location isn't correct, the pictures aren't theirs or straight-out the person is posting from Nigeria, some will still ignore it. What could anyone every do to help those people? Delete the ads? What about those that would take head of the information posted or could really use it?
So those unsuspecting that have contacted the person before the user is banned or anything pointed out aren't going to be helped by simply deleting the ad.
Deleting it isn't going to help us identify them in the future so we still need the information to cross check. Those that were scammed would benefit from us having the ad available to post on the BOI.
If the ad is simple gone then the resources we have to help provide any evidence of someone being wronged would disappear as well.
Saving bandwidth wouldn't happen by blocking the public view.
Blocking the public view would not share with others that may just be getting ready to send funds to the person that something is wrong.
I think it is more important to get the information available to be seen as fast as possible then deleting it. Regardless if it is banning the member for a rules violation, posting that the user is using pictures that aren't his or if they are posting from overseas.
I don't believe simply deleting it to protect the few who can't read is a better direction to go than informing others that can.
There is so much information in ads that can be very valuable if they are completely removed, it's a loss.
Many shill accounts for members have been linked to bogus accounts because we still had the information from their ads pretending to be someone else. Many regurgitate the same information that could be linked to their original accounts.
I think its a benefit to keep much of the information available.
I know if I was working a deal with someone I would be more appreciative that the information I might need is posted where I could maybe find it. I might not even know if the ad was simply deleted.
It's possible, I might not even know a BOI thread was started in the middle of my transaction, comments were made on the ad or that the member was banned if we were contacting each other with just email by that point. I have a greater chance of finding out and acting on the information then the ad simply vanishing.
Let's say we deleted a questionable ad or even a downright obvious scammer ad right away. A month later on this forum or somewhere on the net that person starts a new account. They use the same email address they used in the ad removed. A buyer doing is best to research searches the email and finds nothing.
Let's say that ad was kept and someone posted the pictures are stolen and the buyer is scamming.
I would rather that information was there for the buyer searching than the challenged soul who still wants to buy from the person after the warnings where posted in that very ad.
A bit more time-consuming? Sure. Worth the extra effort? I think so. 
