I would think the biggest source of migration is the "tier" of people making massive salaries (like 300k-1mil) is much larger in CS than Engineering, although its not even close to a median outcome from studying CS. But I think this kind of has a lottery effect where people will take their chances in hopes of this, or hear about it and overestimate how common this is.

I don't really buy the idea that the average Engineer Major has near industry level skills in Software from side-projects unless they are a doctorate from MIT or something. I majored in MechE at a US-top 40 uni and I easily found roles in group projects they wanted me programming micro-controllers just because I was half-decent at basic C++. Its a whole ass thing you'll have transfer a lot of dedication and grind to and pretty competitive.

Other smaller groups of people might just think it fits their work habits / learning style a lot better.