I will happily accept payment for reading and responding to e-mail. I will not pay to send one, and I don't know of any cases where I feel the need to pay for someone's initial reading of an e-mail (I may want to pay for their attention, but that will be a negotiation or fee for a thing, not for a mail).
What _might_ be valuable is a referral service - a way to have someone who (lightly) knows you and who (somewhat) knows the person you want to correspond with, who can vouch for the fact that there's some actual reason not to ignore your mail. No payment in money, some payment (and reinforcement) in reputation.
Basically, e-mail isn't the problem, the variance in quality of things for me to look at is the problem. Curation is the answer, not payment.