Sure. Of course. Not being allowed to disconnect them would be ridiculous. But do you want to keep an eye on the market every day, and run to the breaker to turn on an off your inverter? No. So you need a solution for that. Then a battery is much more interesting.
Completely agree. I mainly mention it to dispel any notions that solar panels can expose you to financial risk due to negative energy prices. This is trivial to address. Negative prices should only be a concern for plants that can not be quickly or easily shut down, like thermal plants (coal/gas/nuclear).
You could implement something pretty easily with a relay or contactor and an ESP32 and a way to monitor the spot price, or just buy a system with that feature already built in.
That's the entire point of Home Assistant, I'm currently writing an integration for my electric company. I'd argue the college junior programmer would try to do it from scratch instead of leveraging the solution that gets you 90 percent of the way there out of the box.