The only way that this would be remotely feasible is if you were able to remotely turn on a user's camera - which won't happen and wouldn't be taken lightly by the end-users.
Ofcourse - all of this doesn't include the cost of awareness that it would take just to make remote use of eye-tracking. You say "tens of thousands" of eye trackers are on the market. With 7billion+ people in the U.S., it's highly likely that you wouldn't receive one person using an eye tracker in the next 10 years - in which you would need hundreds just to make a reasonable estimate on potential site adjustments.
I get what you are trying to do, but the market just isn't there. A better way would be user predictions - or predicting user actions and engagements. That technology is around but not heavily used yet in analytics and would be able to make similar predictions.