First off, if you're not using the player's headphone output to drive headphones, you can (outside of academic interest) ignore everything said with respect to output impedance, DC blocking, and things being different with different headphones. You'd instead be looking at the same factors with the output of the amp you're using, not the output of the player. The considerations are primarily whatever is driving the headphones and whatever is doing the digital/analog conversion—though there's not much to go that wrong for D/A except maybe some noise / hiss, for modern audio electronics that are built sensibly.
Line-out to E11 means you can forget this stuff. E11 has low output impedance including at 0 Hz (DC)—no problems there. More or less, the input of an amp behaves electrically as a large impedance so there are few effects and interactions with respect to the player's output.
A DC blocking capacitor is used in this context as kind of an engineering compromise or solution. Pretty much, you don't want to output DC voltage into headphones, especially small IEMs, or you'll burn them up. More than some low tens of milivolts is maybe bad. Depends. There are various other ways to prevent DC from being output to the headphones, different amplifier designs that could be used. Most of the alternate schemes may require additional complexity, more parts, higher power consumption. Putting a capacitor on the output of the device means that if you plug in headphones, any DC that would have gone into the headphones, instead goes across the capacitor. The drawback is that you need a capacitor, there will be some amount of bass rolloff (less with a larger capacitance value), some amount of distortion (less with certain capacitor types). Because of size and cost limitations, electrolytics are usually used, but even then, they're usually too small in capacitance to avoid some non-trivial bass rolloff with 16-32 ohms headphones.