I agree.
But...
Reading the OPs post in the most favourable light, it sounds like what he'd like would be the existing "free" service, but to have a wait to pay for it in an attempt to ensure it'll still be worthwhile for the company to keep it running long term.
They say 'the cost for an "active but lightly used database" is somewhere between $1 and $2.5 per month.' so it's at least the right order of magnitude.
But one single support call to an entitled "paying customer" blows away any benefit here, so you're probably right that it's a bad idea.
But accept $2? Now you’re knowingly taking money from a cheapass, and you owe them some level of service, support, and commitment as they’re paying you.
Free customers are worth so much more than $2 customers.
Guess you would have to do yearly billing to not have it all eaten by processing fees.
Compare local bus tickets vs taking a cab. The taxi costs 50x more, but in the best case scenario, they provide exactly the same value! If the bus is late, cold or overcrowded, I have no expectations to get refunded or even an apology. I just have to suck it up. This happens rarely enough that I still accept it and hand over my trust to them.
There is no illusion that my $2 bus ticket alone is enough to keep the bus running, in contrast with the cab.
(Bus companies having a tough time to profit is an orthagonal issue, taxi drivers struggle a lot too)
Nobody wants a customer who values a service like that at $2.