One of the weaknesses of "Advertise On This Site" was that it didn't cater for the typical "small publisher" who has a few different domain names.

You could pick ONE logo to show on the landing page. It had to be the same logo whichever site the potential advertiser wants to advertise on.

No, that was never going to work, was it?

In regards to continuing site-advertisement options, Google says:

<<We will continue allowing advertisers to placement target (formally known as site targeting) on specific URLs as well as positions within sites and bid on a CPC and CPM basis.

Advertisers can also use custom channels to select certain sites within the Google Content Network>>