Faint speaker hiss

No this is not normal anymore. I just checked with my own P3ESRs (driven by an old refurbished Quad 405-2 and just a volume control): nothing, absolutely nothing, no mains hum and no noise. It might be different if you are a young girl, of course, since they have better high frequency hearing (I will have to ask my daughter). With very efficient speakers you might just hear something, but not with inefficient ones like these.
Cables do not make any difference in this respect, so they are also out. And since you also hear it when you have disconnected your sources, it is not those either.
So it is the amplifier in one way or another. Do you hear it on every input or only on some?

If you only hear it with your ears 3 inches from the tweeter, don’t worry about it. I hear a slight hiss from my phono preamp ( tube ). If you don't hear anything from your listening position why bother with it?

Have 110db 1 watt loudspeakers running and no noise so while a bit of hiss can be normal in some systems its possible to not have any. Many point to tube amps as having noise but I have found that some SS amplifiers can be even more so.

You shouldn't worry about it given your current speakers but keep this in mind if/when you decide to upgrade or switch to more efficient speakers, e.g., > 92 dB/w/m, etc., since the hissing sound could become more audible. Ideally, the tweeters should be dead quiet if your amplifier/preamplifier - in case of separates, have a properly matched gains but there's nothing you can do with an integrated unit. One could argue this is an indication of a suboptimal design by the manufacturer.

No this is not normal anymore.

This statement is incorrect. With nearly any integrated amplifier a hiss will be heard on that speaker. But it is of no consequence as others have pointed out; I've yet to meet any audiophile that listened to their speakers from only a couple of inches.