I haven’t been able to figure out the use case for DAPs, however.
1. You're not allowed a smartphone with a camera and mobile internet at work.
2. You like a certain earphone. You hate charging two earpieces in a case. You like a certain phone as a phone. Certain phone's manufacturer ditched 3.5mm jacks. You also hate dongles, much less one with a chip in it.
3. You also use it as a music server at home, ex HiFiMans and Fiio X-series with docks that keep them upright; or Fiio M-series where your smartphone can serve as a remote so you need to set it upright on the desk. (vs a phone that now you can't get custom docks for and will also require a DAC)
4. You have a rather high sensitivity headphone in a transportable system that you use at other locations and the DAP is nearly as powerful as the average portable amp you might as well just bring a powerbank than have a DAC-HPamp hooked up to your phone.
5. You also prefer drag and drop for file management for the audio player.
Are they primarily designed for higher end IEMs?
Depends.
If you mean "lower sensitivity, multiple driver custom in-ear monitors," then most of them are.
If you mean "kinda expensive but still very high sensitivity in-ear monitor," then some can still have low noise. Some might have been geared more for lower sensitivity IEMs or headphones (lower relative to IEMs, high relative to headphones in general), and may have a lot of audible noise when you put a low impedance, high sensitivity IEM on it.
Is there a noticeable (audible) difference between the use of an iPhone or iPod Touch and a DAP?
Depends.
Are your IEMs too low impedance that you're causing the damping factor on the iDevice to drop? Or are they too high and not too high sensitivity either that you're cranking it up to the point where the THD+N is noticeably higher? Is the sensitivity too low that you have to crank them up that you're getting higher THD+N?
Can I use Tidal from a DAP?
Some running modified Android can run Tidal I think but if you mean "seamless like my iDevice" stop reading now and never, ever, look at a DAP ever again the same way I tore my hair out figuring out why iTunes wants to load everything when everything doesn't fit and I can't figure out how to choose only what goes in. If you're baffled by all that, walk away. Just walk away. That's a perfect reason for why you're not the target market for DAPs.
Does, for example, a DAP work better as a noticeably higher quality source source to a DAC/AMP than a computer or iPhone? — reading this post over, this is probably the key question.
Depends.
Are you cranking it up high enough to start hearing distortion that is easily audible (for whatever reason, like you hate good hearing or the sensitivity is too low/impedance is too high) or you just prefer a slightly cleaner (or in some cases deliberately warmer) sound?
Are you tired of charging two separate pieces in a small case and prefer dealing with cables? Or are you tired of dongles and just want normal analogue cables?
What makes DAP use different from using an iPhone connected to a smaller portable amp (other than the obvious — one less item to carry)?
DAP : You might not hear or feel the iPhone when a call comes in
iPhone with DAC-HPamp : No mic contact on the DAC-HPamp, so now you have to put that strapped together brick up to your lips; you might be able to run a more powerful DAC-HPamp (vs whatever amp circuit is in many DAPs, which in many cases now, is still an integrated audio chip comparable to some smartphones' audio chips but without the battery-sipping, battery-benchmark reviewer acing limits that phone manufacturers put in there; see Fiio M-series vs X-series)