You're not, it's a legit question. Voltage tells how loud we go, so if and when the DAC gives enough voltage for a given headphone to be loud(which is the case for me with my HD650 and my listening habits), it's normal to wonder if we need to waste money for an amplifier.
Part of the answer is simply that power is voltage times current, and while DACs are the champs of precise voltage to make the accurate analog audio signal, the line out often sucks when it comes to providing current(by design).
The amp on the other hand is supposed to provide as much current as the headphone will be willing to let flow while listening as loud as you want. The idea is for the headphone to be the limiter of current. If that is not the case, then that amp is simply not right for that headphone and your use of it.
Now I hope I'm not overcomplicating things.
If you have candidates in mind for your system, it's usually a good idea to mention them. First because for most predictions of power needs, the specs of the headphone and amp must be known. But also, your post might be seen by somebody who tried them and has some opinion or advice to share.
TL;DR I did not get it, but eventually figured it out (I think) and will probably just have to get a Desktop DAC and Amp :/
OK Thank You very much for the response, I think I get it now.
As for my gear, I want to get the Tin Hifi P1 Plus, a planar IEM. Technically it should be fairly easy to drive, as its Impedance is 22 Ω ± 15% and its Sensitivity is 108±3 dB SPL/mW, but based on reviews it requires a good amount of power to sound best, somewhere around 800-1000 mW. This would mean that I'd need a desktop setup to power it properly, which isn't really what I want at the moment.
Luckily, Topping recently released the NX7, a portable amplifier that has the Specs I listed in the original post, which should be enough to drive the IEM. I specifically listed the specs at Medium Gain (Unity Gain), because at High Gain (+13.9 dB, 21 Vpp/7.425 Vrms) the Input Sensitivity is 1.5 Vrms, which means the amplifier would clip if a DAC at max power (2 Vrms) delivered it a line-level signal at its Input. If the Output Voltage of the DAC is greater than the Input Sensitivity of the Amplifier it causes Clipping, which is bad. Also the Noise Level at High Gain is higher, which isn't what I'd want for a sensitive IEM.
Now I just needed a small, portable DAC capable of delivering a line-level signal to an external amplifier, which I've learnt is kind of rare. Ideally I'd just get an AudioQuest Dragonfly Red ($300 CAD), which is capable of doing just that, but it's way too expensive for what it is IMO and it's SINAD (Measured Noise and Distortion Level) is relatively low, which is bad, as higher SINAD is better. I also came across the EarMen Eagle ($162 CAD), but it's SINAD level is just as low as the AQ DragonFly Red.
Finally, I came across the Helm Audio Bolt ($138 CAD), a small dongle DAC, which, based on this review,
https://www.audiosciencereview.com/...elm-audio-bolt-review-portable-dac-amp.20395/ has a relatively high (Good) SINAD level and based on these reviews,
https://www.head-fi.org/showcase/helm-audio-bolt-dac-amp.25124/reviews sounds, tone wise, pretty good for what I want. Most importantly, according to Helm Audio it's 3.5 mm Out can "serve as the front end source for an external amplifier". So it can operate as a DAC only, delivering full or near full power (2 Vrms) to the Amp, without introducing Distortion into the signal. I've corroborated this statement based on reviews and reviewers' comments I've read.
What confused me was the Required Power and Voltage of the IEM and the Unity Gain, Output Level and Output Voltage of the Amplifier in combination with the DAC.
If the IEM required at least 800 mW @ 22Ω, that would convert to ~ 4.2 Vrms. The Amp is capable of 1200 mW @ 16Ω ~ 4.4 Vrms and 1400 mW @ 32Ω ~ 6.7 Vrms. We don't know what the Power/Voltage rating of the Amp at the Impedance rating of the IEM (22Ω) is, only that it's somewhere between the above values.
Then we introduce Gain into the equation. We can only operate the Amp with the DAC at Medium/Unity Gain (-0.1dB) because of the reasons I listed in the second paragraph talking about the NX7 Amp. The Specs of the Amp state that its Output Voltage/Level at Medium/Unity Gain is 11 Vpp, which converts to ~ 3.889 Vrms.
So even though the amplifier can output somewhere between 1200 mW / 4.2 Vrms and 1400 mW / 6.7 Vrms at the impedance rating (22Ω) of our IEM, at Med/Unity Gain it's limited to 3.889 Vrms.
Think I've just had a bittersweet Eureka! moment thinking about and writing this whole damn thing. Taking into account the Output Voltage/Level, Input Sensitivity, Output Power and Gain of the Amplifier listed on the Specifications Sheet, the Amp can only output those Power values if it's set to High Gain.
So at the gain I'd need to use it at, Med/Unity Gain (-0.1dB), it can only output a max of 3.889 Vrms, because the Input Sensitivity at Medium Gain is 4 Vrms and the only way to get it to output it's max voltage at Unity Gain, would be to feed it that max voltage, which still wouldn't be enough for the IEM.
The only way to solve this issue would be to use the Amp in High Gain and limit the Output Level/Voltage of the DAC to the Input Sensitivity of the Amp at High Gain, so ~ 1.5 Vrms. Unfortunately the DAC doesn't have this function, as it automatically outputs 2 Vrms if the Impedance of the Load is greater than 150Ω, which I'm sure the Amp is.
So basically, I'll have to just get a Desktop DAC and Amp. It's kind of unfortunate, but at least I figured all this out now instead of after buying the DAC and Amp. Thank You very much for your help