Wow, very long thread that happened in just a single day. I've not done this for my own domains (yet; I might never do it, but was tossing it out as a thought), but can see the appeal of why Webmagic/Telepathy and others might desire it. It likely wouldn't be effective for an "average" domain name, but for the very elite domain names, one only really wants to deal with qualified buyers. There are different methods to qualify them, and a cash payment might be another means.
To go to the real estate example that was brought up earlier in this thread by some, one might hold an open house for a $400,000 or $1 million home. That won't happen for a $50 million or $100 million property, e.g. the kind that show up in the Mansion section of the WSJ on Fridays (you'll likely have to show you have a high net worth, or deal with a buyer's broker who has qualified you, etc., before the seller will talk).
Some folks suggested "just put a minimum offer". But, that won't help much if the "buyer" is behind some throwaway Gmail account and disappears after a negotiation (a negotiation that uses time/energy). [such a buyer that disappears after paying $20 still leaves the registrant $20 ahead!]
One advantage of making the $20 payment (or whatever amount) to enter discussions is that the owner will know the real identity of who they're dealing with (as opposed to a throwaway identity), as presumably Paypal or other payment methods will pass the real name/email with the payment.
It's interesting that if you go to GoDaddy and search for a domain (pick one you own), GoDaddy will charge people money to attempt to buy it (fixed amount + percentage commission). So, the GoDaddy "broker" is getting paid to talk to you, why shouldn't you get paid to respond? (or ideally cut out the middleman, and deal directly with the buyer)
Indeed, note that GoDaddy charges that fixed fee --- imagine if the fixed fee was $0, and they only charged a commission for success. Then they'd have many fake buyers using their negotiating platform, wasting their brokers' time (many buyers would back out, too). GoDaddy will charge the fixed fee to qualify their own clients --- i.e. they're not going to "do the work" of sending emails/phone calls unless they know they're going to get compensated....and on top of that they want a percentage commission afterwards. But, that fixed fee is important to them to qualify their own buyers. (probably other buyer brokers qualify in a similar manner, e.g. hourly fee, some portion paid in advance or with a minimum total fee, plus a success fee or percentage commission).
Anyhow, this is getting long, and I had to go to bed soon, but it might be productive to think of pros/cons (some of which are above).
One obvious "con" is that it reduces the opportunity to educate some buyers, who don't understand the value of domains (and are unwilling to spend $20).
Also, "spam" provides some data or business intelligence, which one might no longer get. If domain A gets 30 fake/lowball inquiries in a year, whereas domain B gets 2 fake/lowball inquiries in a year, and domain C gets no fake/lowball inquiries in a year, it's probably true that Domain A is desirable (worth renewing), and more desirable than domain B, and domain C is probably less desirable than domain B.