Illegal? If the record companies were so obviously going to win, they could've obtained a preliminary injunction to stop Suno's business. They didn't, so the service continues.
Suno admitted to train their models with copyrighted music and are now defending the position that music copyrights and royalties are bad for the future of music.
Transformative is one of 4 conditions that the court uses to decide if something is fair use. This question is still in active litigation in the courts.
you're right it's a grey area, but in the field of music specifically, it's some of the most stringent requirements. the more creative it is, the more it replaces the market for the original, the less of a parody it is (not weird al), the more you will struggle to use fair use as a defense. suno generating music hits all the parts of "this is hard to defend" while also being in the the most litigious possible industry for fair use
Fair use encompasses a lot of possible scenarios involving copyrighted works which may or may not be commercially licensed: transformative derivative works, short excerpts for purposes of commentary, backups of copies obtained legally, playback for face-to-face instruction, etc.
Fair use has consideration for whether the derivative work disrupts the market for the original, it doesn't mean you can't use it for profit as we saw with the Google books case.
I guess they are hoping for the Uber outcome where they earn enough money during the illegal phase so they can pay some tiny fine and keep going.