I have no objection, in principle, to people paying to contact me by email. But there are quite a few people, organisations and mission critical bots I might like to receive email from that are unlikely to pay to send it, and whitelisting every email or domain that's allowed to contact me is more of an irritation than deleting unfiltered spam. I don't object to strangers paying but I am quite concerned at missing out on useful emails through erecting the most blunt spam filter imaginable.
I think that goes for most people.
It makes a little more sense to charge for a guaranteed response as LinkedIn does indirectly...
I'm sure I would... as a minimum there's password reset emails, payment confirmations & tickets, old friends and colleagues which I'd want to be certain got through to my primary mailbox.... which basically means my primary mailbox is widely publicised information anyway.
And most people have potential clients, casual acquaintances etc that would enrich their life by contacting them, but certainly wouldn't pay 0.1 BTC to do so, so I'm not sure I'd ever stick pay-to-email as a contact on a business card or website. Those people whose email addresses people would happily pay for tend to be able to pay for assistants to screen their primary contact email anyway...