[Suzu]

Honestly, I'm fine with the thought of the Rider not BEING the monster, but rather having the same source of power. Imho, the concept of Fourze for example was good as it was and it wouldn't have worked with Gentarou being a Zodiarts. Also, about OOO Eiji wasn't a Greeed from the beginning on. He became a Greed because of the purple core medals choosing him. So in theory, he wouldn't count as a rider actually being a monster. Also, Eiji was the only Greeed who could control his desire up to a certain point, so in the end, he remained a human on the inside and never fully turned into a monster.

Actually, as for the tear marks, based on that theory, I guess Fourze would have those, if the helmet wasn't completely black. Because even though Gentarou didn't have to suffer as much as many other riders, Gentarou also had to face a lot of hardships on his way.
Besides, there's more riders who don't seem to have them then Fourze or at least they are not as recognizable? Gaim, Wizard, Decade and Den-O for example don't seem to have them or at least not as easily visible like others, despite having a good background story for those.