Phoning home is not an Amcrest-specific thing, all of my cameras (I have a handful of Amcrest and D-Link cameras, and one Reolink camera) try to do that. I've put them all in a separate VLAN which can't access anything, not even DNS. The NVR software lives on a different VLAN and is able to open connections to the cameras for recording.
This setup works perfectly. Most importantly, the cameras all work fine even if they can't phone home.
Some of them are starting to exhibit mechanical failures - I have one pan/tilt model where the connection between the camera and the rest of the unit has broken, and I have another where the mechanical IR filter is starting to stick and sometimes fails to engage or disengage. I think these failures are primarily age-related and I expect that my Amcrest cameras will eventually start to fail in the same way.
These days my main considerations are whether the camera can serve up an RTSP stream. I do all of the motion detection/notification/recording/viewing/etc via Blue Iris.
For a home wireless router, you can buy a supported device and install OpenWRT. https://openwrt.org/supported_devices
I believe I also accomplished the same thing with an Asus router/AP running DD-WRT, but that was a long time ago.
Not to mention the cool toys you can setup to see what is happening