.....There is no conceivable reason why macOS High Sierra cannot run on some older Macs. The specifications shape up to the basic requirements but Apple in their wisdom deem selected machines to be too old to support the installation of macOS High Sierra or macOS Sierra.
This a critical situation as support for Yosemite has all but ended and the same will apply to El Capitan twelve months from now. My early 2008 24" iMac falls in to that catch zone as it cannot 'officially' run anything past El Capitan.
There is an excellent 'Hack' available in patchers for both Sierra and High Sierra written by dosdude1 and are available to download
Both work brilliantly on some older Macs otherwise unsupported by Apple. There is an issue where some wifi cards are not supported. This was the case with my early 2008 24" iMac but was fortunate to source a supported wifi card from a dead late 2009 iMac and just swapped it over. Solved.
So my early 2008 24" iMac is now dual booting Sierra and High Sierra with a significant performance improvement than when it was running El Capitan.
On to my late 2009 21.5" iMac it was a painful and hair pulling experience installing macOS High Sierra which Apple claim is supported
As in one of my earlier posts it required going round the houses to get High Sierra on a supported machine
1) Installed macOS High Sierra Public Beta in a virtual environment using VMware Fusion 8.5
2) Once installed shut down the macOS High Sierra Public Beta virtual machine.
3) Mounted the virtual image using Paragon VMDK Mounter.
4) Cloned the mounted image to a physical partition using Carbon Copy Cloner 4
Might as well build a Hackintosh!!!