They also tend to only install units that you can't buy directly and only quote for total cost not parts and labor so you cannot easily tell just how much they are charging for the labor.
It must make a difference otherwise they'd provide the breakdown when asked.
I suspect most consumers don't know how much the appliance should cost, it is a complex piece of machinery. But the labor part is easier to reason about.
So seeing $12k all in to install a heat pump might seem reasonable, people will shrug and say heatpumps must be expensive, but if they see that's $5k for the heat pump and $7k for the labor then it doesn't seem so reasonable.
And there are alternatives. You can buy comparable units from other manufacturers directly and shop for labor only (harder to find but not impossible). And there are sealed DIY units you can install yourself.
The answer to this, assuming the breakdown was actually honest, is exactly why they don't typically provide a breakdown. You would see an hourly labor rate that would make a lawyer blush. There's just something unpalatable to most people about seeing a $200-300+/hr labor rate, especially considering that the average person paying that rate probably make closer to $20-40/hr.
