While there might be some design merit in a DC coupled power amp there is the problem of Dc drift which is sometimes controlled by a servo circuit to hold the amp output at 0 volts. Unfortunately servos can intrude on the sonic attributes of the amplifier. There is also the inherent problem of real gain at Dc, typically 26 db and this means any dc in the signal path will be amplifed by this amount of gain.

It is therefore adviseable to use a high quality film foil coupling capacitor at the input of the power amplifier to block any DC, pops ect that can result from the source.

People complain about capacitors a lot.

Finch and Marsh wrote a very good article on this topic with mods than can be done to preamps and power amps to minimise most of the negative effects.

If the coupling capacitor is chose correctly (and the capacitor in the feedback path) it should introduce little phase shift in the audio passband.

It is worth noting that a typical recording is processed though many stages that introduce some phase shift so don't let anyone pull you chain about phase shift in your modern day power amp!

I would also point out that some of the most expensive pre amps and the most well regarded are capacitively coupled but of course cost is no object with the parts quality in these designs! Unfortunately mass market consumer audio equipment often uses parts chosen on price and not sonic performance.