That would be awesome, but it would also make it way harder for Google to offer a free tier in the first place. 300 free queries per user per day is a lot more than 300 free queries per developer per day, so it might be a mistake to make that usage pattern even easier.
Though maybe they could just place way stricter limits on requests placed via API tokens obtained this way? That would probably work. But it would also sort of defeat the purpose of having users use their own API tokens. If everyone's going to need to pay to use your app anyway, you can just have them pay you to use your API token and gain an easy source of monetization in the process.
For FLOSS use cases, the author may not want to deal with everything that comes from collecting money from people. So it's still useful to let users pay Google directly for their usage.
Though maybe they could just place way stricter limits on requests placed via API tokens obtained this way? That would probably work. But it would also sort of defeat the purpose of having users use their own API tokens. If everyone's going to need to pay to use your app anyway, you can just have them pay you to use your API token and gain an easy source of monetization in the process.