It could be automatically recorded by chess.com during the games, and export could be the standard PGN (without the time data), or PGN+Times.
My understanding is that they already track the time just don't present it. I can't recall if they are planning on adding it, or an option to include it, in the future or not.
Isn't it wonderful that hundreds of years ago people had the foresight to devise a system to record the moves of games.
Many times I have heard GMs like Melikset Khachiyan say things in the videos like "I don't if they were in time trouble...".
Wouldn't it be great if the PGN spec could include actual time of each move as well? And isn't it something which today would be easy? It could be automatically recorded by chess.com during the games, and export could be the standard PGN (without the time data), or PGN+Times.
For example:
1. e4 e5 2. Nf3 Nc6 3. Bb5 a6
could be also available as:
1. e4 {0:01} e5 {0:05} 2. Nf3 {0:10} Nc6 {1:23} 3. Bb5 {0:15} a6 {1:35}