It would be far easier (and cheaper) to modify 10 pairs of wired headphones to have a Lightning plug and D/A converter than it would be to modify a single iPhone.
While a very nicely-executed mod, it's also a very difficult, expensive mod that compromises the water resistance and functional integrity of the primary bit of equipment, voids useful warranty coverage, and makes swap-out/replacement of a malfunctioning device impractical. Apple would refuse to repair it (even out of warranty), and the job has an approximately 2-year lifespan before upgrading to the next model.
By comparison, modded headphones can be used with nearly any iPhone, iPad, or iPod Touch. Although the headphone warranty would be equally void, the need for warranty service is far less likely, and the effort and cost of reproducing the mod should the headphones have to be replaced is far, far less.
Of course, using/replacing dongles is even cheaper and easier, but this is clearly the principle of the thing. I think the pursuit of a dongle-free existence is a Quixotic quest, but we all have some affection for that dear, fictional knight.
As a former recording/broadcast engineer who modded a fair amount of gear back in analog days, built countless custom adapter cables and interface boxes, and has been accustomed to making heavy use of adapters and dongles for, well, forever...
If one of my bosses had suggested I mod their iPhone rather than mod their headphones or use a dongle, I'd have replied that it's an impractical solution compared to the alternatives. The boss could still have gotten his way, of course. I'd have shrugged at the end, said, "It's your money," and proceeded with the project.
The only reason, imho, for the boss to insist on modding the iPhone would be for the bragging rights. I did have a boss like that; I can imagine him showing off his one-of-a-kind iPhone to all his clients and fellow musicians, producers, and songwriters. I'd even have gathered some personal glory - he liked to impress people with the talents of his hand-picked staff. But most of the time, even he would have made the practical decision.