Those are some strong statements. While the internal PA can drive my headphones, doing so drives me nuts.
In the past, on-board sound chips were bare bones and were stuck where ever there was room on the motherboard. HF noise gets coupled to the analog outputs. You may not hear it in a low impedance load like a headphone, but it becomes more apparent when plugged into an amplifier. My old Dell workstation at work is absolutely horrible and most laptops I have used are even worse. I can hear the mouse move on all of my laptops!
I have met far more horrible built-in sound solutions than not. Sound cards tend to be a lot better, but they still will couple noise simply because the EMI environment of a PC case is that bad. If I crank-up my desktop speakers to 1/2 or more (plugged into my sound card) I can "hear" one of my 3 HDs popping and large updates to the UI make squeaking noises.
In an office with CPU fans and whatnot and reasonable speaker volume levels, it isn't really a problem. For headphones, I prefer the black background of a decent DAC.
The real problem is that you don't know if a particular combo is good or not. Indeed, even some much-hyped add-ons (like the Essence STX) can suffer pretty badly from EM noise leakage in certain slot configurations.
At the same time though, it's pointless generalising 'all onboards suck, buy a DAC' because onboards have improved quite a lot as of late in general thanks to various Microsoft edicts for compatibility.
Some are bad. My 2010/2012 Mac Pro's, if I choose to use a headphone to listen to them thru the front panel socket, are unlistenable - there's just too much EM leakage. Same goes for recent Air's and Macbook Pro's to a lesser degree, but still enough to warrant a DAC. But the vast majority of Windows desktops and laptops (including a couple of MSI and Asus-boarded DIY's, and I'll qualify here that I don't keep laptops beyond about a year, nor desktops beyond 2 years - except in the case of the it's-still-2009-layout antique like the Mac Pro), I'm pretty happy to jam a headphone into and listen, unless I'm doing a bout of critical listening or monitoring.
Which is why I said listen first. His might suck, it might not.