That's really interesting! I've never had that problem; conversely I tap into the singing part of my brain to keep flow (albeit I suffer more from cluttering than stuttering), and do reading and tongue twisters with a metronome. I do however see it a bit in soloing (fortunately I'm mainly classical), where the ideas flow as chunkily and rapid-fire as my speech, so I can't rule out a connection. I can really only recommend that you check out the studies at [Center for Music in the Brain](https://musicinthebrain.au.dk/), if you're more interested in the speech/music coupling.