Amplifier headroom to me is the short-term power available above the long-term specification. I do not consider a low number good or bad, just something to include when making a purchase decision. Conventional amplifiers are all over the map. Some amplifiers specified up to 6 dB (4x) of headroom, while others essentially 0 dB. The former had a very "weak" power supply or insufficient thermal management to sustain that power for a long time. The latter typically had very "stiff" or regulated power supplies and thermal management (e.g. heat sinks, fans) to sustain the power long-term. Then you decide based upon your budget, listening habits, speakers, etc. whether you want a 100 W amplifier with 6 dB of headroom or a 400 W amp with 0 dB headroom. Neither amp is good or bad, and the choice is not right or wrong, just pick the one most appropriate for your system and meeting your other parameters (like cost, size, weight, etc.)
Of course, manufacturers may choose to rate to emphasis different parameters, and that can affect headroom as well. Derating the 8-ohm power to achieve a doubling in power at 4 ohms, often deemed desirable by audiophiles, can lead to greater headroom. The exact same amp could be rated for more power at 8 ohms and thus have lower headroom. Similarly, a manufacturer may want to specify very low distortion at rated power, leading to greater headroom than if they chose to specify higher distortion and (higher) rated power. All sorts of variables.
Class D output stages switch between power rails so a tightly-regulated supply reduces the chance of amplitude modulation with pulse width (distortion). High sampling rates and feedback control that issue, but the way they work headroom is not usually a desirable trait in a class D amplifier. Arguably not in any amplifier, but there are trades to be had, though by and large class D amps achieve greater power and performance than many (most?) class AB amps. Choice can be good.
FWIWFM - Don