You're not really describing Shareware (though in practice it may not have been a whole lot different). Shareware was software distributed under a try-before-you-buy license but the license actually required you to pay if you continued to use the software beyond a certain time period.

Did this make a difference for most users? No. But, when I wrote shareware, I usually got one or two 4 figure site licenses per year from companies for my product. It was just a sideline but the difference between pure donationware and "you're really legally required to pay for this" did make a difference.

That said, today I'd probably just do it as open source donationware though the money wasn't completely trivial for me at the time.