Phase response fallows the transfer function of the coupling circuit. In certain applications, a designer will look at this. In small signal amplification designs, not much attention is paid to this other than measuring the effect afterwards for bench marking on a datasheet.
You have a very strange view on how products are designed. Of course, any half-decent designer will determine the value of coupling capacitors, according to the surrounding circuit's impedances and a targetted response.
The capacitor is the cheapest method of AC coupling. Cheapest as in the cost of the part itself, and design considerations involved in compared to the better, but more expensive method called transformer coupling.
It is known since ages that transformers are very unperfect, with limited frequency response and distortion issues. For many years, it was just about the only option in some circuits, but today, there is no objective reason to use a transformer in an audio circuit. Today ransformers are used for a supposed euphonic quality, for respect of a vintage circuit or for marketing reasons.
With solid-state electronics, there is no circuit where a transformer could not be replaced with a good capacitor.
Transformer coupling is superior becauese the designer can make the transformer specs in circuit exceed the bandwith response curves the capacitor circuits can achieve.
It is extremely difficult to increase the frequency response of a transformer, because for increasing the LF response, the inductance must be increased, which results in increased leakage capacitance, which in turn reduces the HF response. In other words, a compromise must be found between LF and HF extension.
Conversely, increasing the value of a coupling capacitor, for lowering the LF cut-off, results in almost no effect on the HF response.
But the best method of coupling is always DC coupling because it does not limit bandwidth
Is it really necessary, or even desirable? What's the point of passing 1Hz at 0dB, when no transducer can make any use of it?
nor add distortion, besides self noise in resistors, that can be selected for better noise profile.
How can DC coupling improve noise?