But quality of life is much higher for the software engineer, so assuming it's just as easy to be both, pay would need to be much higher for the plumber to incentivize people to do it.
Is it? I had some plumbers doing work in my house last year. They were pretty happy guys. Playing music on the radio, singing while they were at work. Meanwhile i'm here sitting at a desk all day.
A huge potential loss is in the marriage market, where being a plumber isn't as marketable as doctor/engineer/lawyer/financier. Also, big loss is wear and tear on your body from manual work, higher risks due to driving all the time, variable hours due to emergency nature of work, and finally, it doesn't scale well. Plumbers are well compensated, but is it enough to give up the chance to earn much more in businesses that scale up much easier?
The primary difference is the time it takes your salary to ramp up before it plateaus. Far fewer plumbers will not be making six figures (real world money, not StupidValley monopoly bucks) after five years or so in the workforce. That said, the work environment might be worth the money IMO.