"but I think eventually AI will be able to write and record a song, better or even equal to a real human's input."

Sure, that's why we should not waste time and stop playing music immediately. Same goes for sports, video games, books, puzzles, drawing, painting, sculpting, writing and many many others. Because AI can/will do it better, and some might argue just live "life" better than pathetic us smile

"We can mourn the human creative process".
In chess, machines were able to "win" over humans with ease for decades. Yet, we still enjoy PLAYING that GAME and praise our best.

The question which should be asked talking about this: "press one button songwrite and record"
Does this process of "button pressing" makes you a creative person? If that's the goal of course....
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2044... Full time creative job opening. Professional button presser. Pre-requisite 4 years of college.