As usual, if there's no headphone jack, I won't buy that device. Privacy isn't even the deal breaker there. Latency and the ability to use my favourite set (Sennheiser HD600) are.
As one data point, the headphone jack-having iPhone would drive 26.39 mW into 33 ohms, which means that at max volume you'd be damaging your ears at a volume of around 100dB with the 300ohm impedance and 105dB/mW SPL.
So yes, the previous poster could conceivably be doing the thing that they said they were doing.
Their sensitivity is only 97dB/mW. But I think it's more complicated than that. The amplifier might be able to deliever 26mW into 33 ohms but can it deliver that into 300 ohms? It would have to be able to produce high enough voltages. Also the impedance goes up to almost 600 ohms at the resonant frequency of the headphones, requiring even more voltage [1]. You'd obviously get some sound and it would probably even be loud enough, but there would likely be a significant effect on the frequency response and possibly more distortion that you'd like.
When at my desk, I plug in through a Mont Blanc FiiO for my Beyerdynamic headphones. Makes a big difference with some audio. Wireless buds are obviously already a step down from wired, and one step further from amplified cans. And yeah, I'm an outlier and want to be.
But there are combined DAC/amps that will use lightning connectors, so if you use an external amp, you might as well use an external dac/amp instead and get audio quality that is certainly no worse than a random android phone, and possibly better.
When the volume is set quite high (near max setting of the phone, definitely unhealthy for long-term use), it doesn't hold a candle to the Topping DX3 Pro v1[0] I use on my desktop. Important: I don't recommend the v2[1] that's currently on sale, as the measurements aren't anywhere as good. They did destroy the product with the amp redesign they did to get around a high early failure rate hardware problem on the v1 that they were never able to debug. I would suggest the JDS Atom + Atom DAC set or the Topping DX7 Pro instead, cheap (yet powerful well measuring) and expensive (but balanced and ridiculously well measuring) respectively. Or a Schiit Hel for a very portable usb-powered solution for the laptop backpack that also has mic input.
But at lowish volumes (used most of the time, don't destroy your ears!) then yes, phones tend to have reasonable headphone amps in them. With decent power output and lowish output impedance. Unlike most computer motherboards, which have excessive output impedance and out power is so low I'd call anemic, when not flawed in other ways (noise due to poor isolation, or non-flat frequency reproduction due to shit implementations of aliasing filters).
I mostly connect the headphones to the phone to play rhythm games like Love Live sif, allstars or idolm@ster deresute, mirishita. My phone (chinese and a few years old) does very successfully drive the HD600 to a pleasant output while playing these games.
As an aside, I absolutely recommend Sennheiser HD600 to anyone who wants a durable (plus tool-free modular with good availability of parts, and compatibility with HD580/58x/650(aka 6xx),660S parts, thus effectively forever) all-rounder open back headphone with a focus on accuracy that's cost efficient and extremely comfortable. Plus they've been around for a good two decades, thus there's no shortage of reviews to base a purchase decision on.
It’s still kicking around, still works, but I switched to easy to drive IEMs for on the go listening so my biggest problem these days is getting the volume quiet enough.
I felt cheated after falling for the mass hysteria, which lead me to acquire my first set of SR-60. It didn't take very long to realise how uncomfortable they are for longer listening periods, or when the cable turns into a tangled mess, and the special hell, when you have to replace the earpads.
