Not 100% - you do need internet for things like schedules as that relies on a NTP for time. And firmware upgrades.
Although you could run a local NTP server on e.g. a Raspberry Pi or some routers (e.g. with Merlin firmware)
You can get an accurate time source using a GPS receiver - they are very inexpensive these days. That, with a minimal computer such as a Raspberry Pi, provides a reliable and non-internet-connected NTP solution.
One big question would be can you get along without any external access when beyond WiFi range? I love to get the Pushover notifications . . .
Interesting question. You need the Internet at one point or another with all of them because you either need to get the software if it’s open source, or if it’s manufactured you need to register. Even with HE, that can run without Internet, you initially need the Internet to register it.