Setting a minimum offer does almost nothing to stop low-ball inquiries. People just fill in $987654321 for the offer and in the comments say that their real offer is $100. Anyone who gets a decent amount of inquiries knows this. Charging $19 doesn't even completely stop it, but it comes pretty darn close. I've seen people pay $19 to make a $10 offer on an LLL.com though. Go figure.
Anyone who owns an LLL.com knows they get several inquiries a week, maybe more. Now imagine owning roughly 10% of all LLL.com domains in existence. Then add in several LL.com, hundreds of dictionary domains, hundreds of surnames, hundreds of city names, and more. The amount of spam and low-ball inquiries is astronomical. Wading through that flood trying to pick out the ten people a year who will actually meet your price expectations is not only daunting, it may cause you to miss legitimate inquiries. One thing is certain, if you are serious and willing to pay high retail for a domain there's no chance that paying $19 to ensure that your offer is heard is going to scare you away.
I find it odd that some people think the owner of one of the most valuable domain portfolios in the world is doing this to get rich $19 at a time. As the OP put it... REALLY? It's not about making money or about greed, it's about saving time and not having to hire an army of people to sort through spam and low offers. The only way to make someone think twice about pressing submit is to make them take out their wallet first.
This isn't like a car salesman whose job it is to show you around, tell you the price, and make the sale. This is like walking on the sidewalk in front of someone's house and spotting a Monet through their window, knocking on their door and speaking to them at length about it, and then offering $100 for it. How many times would you let that happen before you charge admission or hire security? Hundreds of times per day? I think not.
I personally find it more distasteful when someone thinks they are entitled to take away your time just because they like something you own, than when someone tries to qualify leads in the only way that actually works at scale. Rick Schwartz qualified leads by ignoring people and being rude to them to see who didn't give up. To each his own... I'd prefer to pay $19 than to have my patience tested.
Nat responds to all inquiries personally, except of course for domains that are under a brokerage agreement. Anyone who knows Nat knows he is very humble and gives freely of his time to causes such as the ICA. To suggest that he's doing this out of ego or any other bad intentions just shows how little you know about him and the reality of owning a large, premium portfolio.
There's only two ways to deal with it: reduce the number of inquiries by adding a hurdle or staff up and run a big operation. He chose the former... and that's his prerogative. The system stopped you, a wholesaler, from making an inquiry that almost certainly wouldn't have been accepted anyway. It saved your time, it saved his time, and what do you know... it didn't cost you $19. Just as it doesn't cost most people.
I realize it may make you feel snubbed that your offer wasn't heard but that isn't the intention, it's just to save time. If you want to PM me the domain and your offer I'll pass it along to Nat and I'm sure he'll respond. Just know that he doesn't sell wholesale, so unless you're asking as an end user or on behalf of one, the answer will almost definitely be no.
I've worked for Nat for eight years so I'm speaking from experience. Although let me be clear that I'm not speaking for Nat nor as a representative of the company, these are my words, opinions, and observations.
P.S. - Check out DomainAgents.com, they've been doing this for many years with great success