This smelled like one of those things where they've applied a certain behavior to an entire class of widget for consistency's sake, and TextEdit just happens to use that widget. If so, it'd be controlled at the system settings level.

Sure enough: System Settings -> Keyboard -> (under the "text input" area) Edit... (button next to your primary keyboard language) -> toggle "Show Inline Predictive Text"

If you want to easily switch between having it and not, I bet you can set a second keyboard with the same language but a different setting there and use the quick keyboard switcher widget/shortcuts (I did not try this, though). Or there's probably a way to shortcut it with AppleScript or some other automation thingy with ten minutes of effort (mostly googling).