I am very fascinated by how people mix these songs together, such as DJs often do too. I am convinced Scaler’s capabilities ought to play a role in this, detecting chord sets from different songs that would allow for them to be combined, even if transposed first. Or are the chords in pop/rock music so common, that different artists inadvertantly use the same chords which then can be blended between songs?
Must have something to do with Billy Idol, LOL
BTW, I never knew that Steve Stevens was the third man in WHAM! 
Funny, I’ve done so much of this stuff across my corporate work (Sydney Fireworks etc) and my time as a DJ. In this instance we would call this a ‘Mash Up’ which is more DAW based and does focus a little more on the compatibility of chords, rhythm and tempo. A DJ however really does focus more on matching BPM, then instrumentations (all the whilst making sure they aren’t mixing a house type four on the floor with a trap 2 step style beat) and finally using their ear to ensure that any musical elements don’t clash. The easiest thing is to mix an intro into an outro which in electronic / dance music terms are usually sparse for a reason. The big DJ’s would always say: Davey, just give me beats for 32 bars and then roll out the groove for 4 mins then give me 32 bars out with just beats!
Today we have more automated tech that allows for one button mixing but the modern great DJ’s still rely heavily on their ear.
As for your point of software to help mashups (as excellent DJ mixing software is there in abundance), there is something there but is very complicated given the amount of things it has to consider.