Well if they give it out for free (aka they pay for it), asking you to register is a reasonable ask. It's not a public service funded by taxpayers.
Exactly this.
If you present me with a form and a submit button then I expect the input to go through and a result to be presented.
If you don't want to present me with results before login, then put the form behind the wall too.
Simple.
They have other options... rate limiting, serving (more) quantized to non-registered etc. etc.