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Create a system that encourages creativity, but also keeps you on beat - Wii Music had a neat idea of letting the player play the song however they want. But since the game lacks a proper score or grading system, it ends up achieving the opposite of what it wants to do, and encourages the player to just make random noise instead. So let's make a new system. You can choose any instrument you want for a song, and play the song how you want. But you're graded and rewarded for improvising while staying on beat. Meaning, the more stylishly you improvise, the more points and higher grade you'll get so long as its to the beat of the music. This would be a better system because it actively encourages you to want to play the song different ways to try and get a different or better result.
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Get, or make music people care about - Wii Music suffers from a small, and poor selection of songs, most of them being lame public domain stuff or NES tracks. You're telling me that Nintendo, who was swimming in money from Wii and DS profits, couldn't get actual licensed tracks that people cared about, let alone the original recordings? With this new game, Nintendo needs to bust out their wallet, and license actual well known songs that people would like. Or hell, just go the Bemani route and produce the bulk of the soundtrack in-house. A diverse range of genres should be covered, Funk, hip-hop, Pop, J-Pop, Nintendo, Rock, electronica, etc. A music game is only as good as its soundtrack, and if there are no good songs, then what's the point?
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Up the presentation - This isn't the Wii era anymore. The plain, Apple-aesthetic is not going to work for Switch era anymore. Menus should be colorful, gameplay should be flashy, and the game needs to be eye-catching. It needs to be something you'd want to play out in public with friends.