Headphones are great for minimizing issues of room acoustics, but they are not eliminated. Many people swear by various headphone amps and DACs, but the magnitude of difference these components could possibly impart are still pitiful compared to the improvements made possible by controlling the noise floor of the room you're listening in.
This is why in any situation with ambient noise (e.g. planes, trains and open plan offices) the highest quality audiophile headphones on the market right now are the Bose QuietComfort series.
Active noise cancelling headphones are hardly an audiophile's first pick. Almost all NC headphones introduce audible white noise. They are also ineffective at blocking voices in the background.
Earplugs are significantly cheaper and more effective at blocking noise.
The point is that the sum of added and reduced noise is smaller in the noise cancellation than in non-noise cancellation, unless you are in an optimized environment.
The problem is that voices or crying babies will be more audible in a noisy environment when using active noise cancelling headphones because they only effectively attenuate low frequencies.
you're not going to hear the 'room acoustics' on headphones surely. you may hear some ambient noise from the room if it's not sound-proofed, but that's not the same thing at all
Acoustic treatments also involve sound insulation. An acoustically poor room can also accentuate environmental noise through excessive reflection and transmission.
Active noise-cancelling is counterproductive to a neutral, balanced sound, which is what audiophiles are seeking. The noise produced to cancel out background sounds will also cancel out the music. It is better to just try to use isolating headphones (Beyerdynamic, V-Moda, higer-end Audio-Technica, Mad Dogs, etc).
This is why in any situation with ambient noise (e.g. planes, trains and open plan offices) the highest quality audiophile headphones on the market right now are the Bose QuietComfort series.