This is an amazing attempt to remove spam, though I feat that scammers/spammers will find ways to abuse it so hard...
Another option would be to give people multiple inboxes which sort their messages by the fee paid by the sender. The user could then basically have a tiered system.
I feat this will restrict actual good people who need to send a message to someone but they can't pay the fee that person requires a high fee for him to see your message.
The only way to abuse it would be to pay in STEEM, in which case as long as your a STEEM stakeholder you still benefit financially.
Yes, the whole point is that not everyone who wants to send someone else a message would be able to. That's a feature not a bug.