I imagine RG considers it unreasonable because they consider what they are doing to be fair use. As such, any amount above $0 could be considered unreasonable.

There is no way that any specific licensing source, or even handful of licensing sources, is comprehensive.

If you accept that this use does not qualify as fair use then in good conscience you can only display the lyrics for which you have purchased a license. That cripples the coverage you can provide by making it too resource-intensive to seek out a licensing agreement for the lyrics of more obscure songs.