One thing I like about watching games live compared to replaying an SGF is that there’s more of a feel to the ebbs and flows. e.g. When a dan pauses, I can deduce it’s a critical junction…and try to figure out why / what alternatives they were considering. (of course they could simply be making a sandwich). The current SGF format doesn’t include move time data.
Alternatively, if backwards compatibility were an issue, I’m guessing OGS servers store move timestamps. Could OGS game playback be tweaked to optionally replay the game as experienced by the players (perhaps with a timescale factor)? I know we can currently adjust playback speed, but it’s still all regular timing.
The Arimaa client has a prominent option to replay moves at the speed they were played, and this is very handy for syncing up a game with a commentary track which only exists as audio. Admittedly, this is a rather unique problem; I’m not sure if I’ve ever heard of audio only commentaries of go games, though I’m sure they must have existed back when radio was a bigger thing.
You don’t need a new SGF format to store move time data, the current one already allows it. OGS just chooses not to include it. It might not be a standard property, but SGF allows custom tags and several other go programs, such as KGS, do include it. BL and WL tags seem to be the unofficial standard.