I downloaded google dialer to try it out, but while trying to remove it the system phone all was removed by mistake.
There is no way to remove it. You may have disabled it probably (which isn't possible either), check in App list for it's status.
Try resetting App preferences too.
yes you are correct it cannot be uninstalled. it was disabled .
but should it be possible to be disabled @Anders_ASUS ?
No, it is not supposed to be possible and we cannot do it on our devices.
Can you still "disable" it ? Can you show us a screenshot of that - "Disable" being allowed for the Asus Dialer.
Yes, it can be disable by instelling another dialer(ported google dialer) , then you get the option to disable the default dialer.
Please improve the default dialer, i have written a post suggesting what features could be added.