Yes, all the screen readers handle implicit labels just fine. As the a11ysupport.io tests show, it's Voice Control software that fails, not just Dragon NaturallySpeaking but also the built-in Voice Control in macOS.
I think the implication is these voice control programs aren't using the accessibility tree built by the browser but parsing the DOM themselves, poorly. It's not really surprising for Dragon since it does hardly anything in a browser without its browser extension installed and extensions don't have access to the accessibility tree. It's more surprising for macOS Voice Control.
They must have fixed it in Safari 18. I'm running macOS 14.6.1 and at the beginning of the month it didn't work but I also just tried it and now it does.
I think the implication is these voice control programs aren't using the accessibility tree built by the browser but parsing the DOM themselves, poorly. It's not really surprising for Dragon since it does hardly anything in a browser without its browser extension installed and extensions don't have access to the accessibility tree. It's more surprising for macOS Voice Control.