I was involved in the last AF1 proposal on the losing side: Douglas with the DC-10.
Without going into sensitive technical details, single engine out performance was a BIG deal. The DC-10 could barely, sort of meet the requirements. The 747 met them handily.
Electric power generation requirements were immense and were a huge deal to USAF. Two APUs were required. Providing the required power in flight with an engine out was problematic for the DC-10. Not so the 747. There were other issues.
Douglas had plans to meet all the requirements, but early on it was clear that USAF wanted a four engine jet. Douglas' role was to keep Boeing focussed while looking over their shoulder and the Douglas strategy became to force Boeing to underbid the contract to win it. It worked. Boeing took a financial bath on the last Air Force One project and tied up a bunch of their best engineers for years to solve all the issues.
And as a reminder, the DC-10 had three engines. A twin could not hope to meet those long ago requirements. And the new requirements are MUCH more challenging.
And as an aside, the 747-8 uses GenX engines, same as the 787. These engines and their accessory gear drive have the ability to drive two 250KVA generators EACH. (That is not what is installed on the 747-8, but could be.) With four engines and eight generators, that means 2 gigawatts of installed power, NOT including the APUs (yes, two APUs are required, each also with BIG generators.). I'll leave it up to the reader to conjecture on what all this power is for, but, yes, all that power is needed to power some of the stuff that will be installed on the new Air Force Ones.
As a reminder, the VH-71 was WAY bigger than the VH-3 it was to replace. Yet it was not big enough to handle all the stuff USAF wanted to include. The same with the new Air Force One. The 747-8 is bigger and more powerful than the 747-200 it is replacing, but meeting all the requirements with that bigger airplane will be challenging. Meeting those requirements with a twin cannot be done. It has NOTHING to do with ETOPS or other engine reliability considerations.