Apple has not previously responded to press inquiries about this subject.
Lest you think that nobody would bother releasing malware to attack such old systems, in recent years malware has been found in the wild that was designed to attack multiple platforms, and occasionally this malware has contained code capable of infecting old operating systems and even Macs with Power PC G4/G5 processors (Apple's processors of choice prior to transitioning to Intel in 2006).
This didn't just happen once; it has happened again and again.
While Apple boasts about the extremely high percentage of i Phone, i Pad, and i Pod touch devices that are rapidly upgraded to each major new version of i OS, such is not necessarily the case with Macs and OS X.
Note: Although this article was written for mac OS Sierra (10.12), much of it still applies to mac OS High Sierra (10.13) which was released in September 2017.
High Sierra's system requirements are the same, except that High Sierra now requires 14.3 GB of available disk space, and a minimum of OS X Mountain Lion (10.8) to do a direct-upgrade installation.
You may, however, still be able to obtain it by calling 1-800-MY-APPLE; in the past, Apple would send a special code via e-mail that would enable older OS versions to be downloaded from the Mac App Store.