Additionally, if the new machine doesn't have identical hardware, specifically graphics, network card (nic), monitor: you still wouldn't be able to dump your system image into another one
I used to believe that as well until just recently. I started reading about the subject and found people saying it was not so. I was very sceptical about this until I tried it for myself. I didn't use remastersys, I used an image from qt4-fsarchiver, but the results were startling.
The donor machine - the one from which the image was taken - was a Fujitsu laptop with a Samsung hard drive, Intel graphics, Realtek Ethernet,Intel wifi, and Intel sound, the image was a Ubuntu partition which was installed in Uefi mode.
The recipient machine was an Acer laptop with a Western Digital hard drive, Nvidia graphics, Broadcom ethernet, Intel wifi (but a different version using a different driver), and Intel sound (a different version but using the same driver), the recipient machine had never heard of Uefi.
The image was placed onto a different partition number on a smaller sized partition. It took a long time to start up the first time, but it did start and it worked perfectly.
The reason it did so is that all the modules it needed to run on the new hardware were already present in /etc/modules, all it had to do was load them. Obviously it didn't run the proprietary Nvidia graphics module, it used Nouveau, but it still worked.
I must admit to being very surprised at those results, but it is a fact so I can't dispute it. Linux is much more flexible than either of us previously believed.