The thing is that the value in this case is not in the lyrics themselves but in the transcription and compilation into a central database. The people looking them up already have a copy - they are listening to the song. A transcription is something they could do themselves if they wanted to put in the effort.
From a maximalist perspective you are quite correct. But from the perspective of how much the publication affects the market for the lyrics I think it is reasonable to conclude that at worst the impact is marginal and in the vast majority of cases it has none at all.
It is not an absolute right either. Even the most hardcore maximalists accept that there are some conditions under which that right does not exist, c.f. Jack Valenti's acknowledgement that it would be unconstitutional if the term of copyright was forever.
Would we expect annotated versions of books to be free? No. Would we expect critiques of movies... with the movies themselves to be free? No. That argument just doesn't hold any water.
I just do not understand it?
The two sides are: artists just can't make it through with a little pay with little sources of revenue, or we don't get our lyrics, tabs, and/or the songs themselves for free. It's a difficult balance where solutions are hard to find.
It's worthwhile to basically see lyrics as poetry. Poets get by by selling poetry (well, few, in this day and age), lyricists/songwriters should also ideally be able to get by.
I think the music industry has to adjust to handouts (eg, donations on their site) and merchandise/performances rather than viewing the song itself as something worth selling.
If there's a barrier to me using the music easily, including unavailability of the lyrics, not only am I not going to spend money on things that make them more money (shows, merchandise, etc), but there are a dozen other artists who are all clamoring to make it easy for me to hear their music.
The song - and attached lyrics - should be a way to get me to buy other things or given them money after, and not try to be "sold" to me.
The Harry Fox agency (harryfox.com) is the industry broker for music publication licensing, virtually everything in the US can be licensed through them.
Looks like LyricFind is owned by Gracenote. Considering that Gracenote got its start by absconding with user-submitted CDDB data, submitted with the understanding that it was GPL'd, that they would pay for lyrics licensing is ironic.
https://en.wikipedia.org/wiki/Gracenote_licensing_controvers...
If the officially licensed rightsholders of those lyrics would like to also make a site, so be it, but it seems they are a bit late to the party.
This rationale would prevent providing a cast list for a movie, because you're publishing the casting agent's work without paying them anything.