Adonis Campaign is one of the more common drip economies that require influence. It certainly has seen its play, holding quite a bit of money on it. It also tends to be rather safe. If the runner trashes it before it is rezed, they are out 3 and the corp is just out a click of the install. If they trash after its rezzed and fired once, its only a credit lost. Trash it after it has fired more than once and it is almost not worth it for the runner. It must be said that the only time to rez an Adonis Campaign is during the paid ability window at the end of the runner's turn. This way the runner doesn't have a chance to trash it, and the corp gets the first income drip right away. Rezing it any time before that just gives the runner a chance to trash it without the corp collecting any money.
The existence of Eve Campaign means it can often be overshadowed. Eve has longer staying power and a higher trash cost, even if it does provide less per turn than Adonis. Combined however, they make a potent drip economy, especially with the likes of PAD Campaign. Adonis lower rez cost is often what gets it in the door over Eve, combined with the greater per turn gain.
That does not mean Adonis is useless however. It is good, reliable money, and even if the runner is just trashing it as soon as they can, then it is causing them to spend money on actions that are not stealing agendas or preparing to steal agendas. It continues to see use, and will continue to be a solid useful bit of drip economy.
(Written during the meta of The Valley, part of the SanSan Cycle. For more reviews like it, visit wyldside.blogspot.com)