Compare to the real world.... if you have an advertising agency, and you shut down the company, do you expect that all ads you've had run in magazines to delete themselves over time?
No, but you would have the expectation that eventually, you'd be forgotten about.
The reason you use billboards for advertising is the chance that the billboard will not be resold to a new advertiser for months/years. You use them because you want to be remembered for so long as you possibly can. Internet just takes it to the next level, nothing ever goes away.