Thanks for the questions and feedback! We thought this was likely to be an area of interest once we launched Cloud Functions + Firebase Hosting, and I can see we were right :)
For now, our advice is to use appropriately short TTLs such that you don't need to manually purge. While origin hits do have higher latency than edge cache hits, even a relatively short CDN TTL (e.g. 10 minutes) can provide massive reductions in load and massive increases in performance. You can think of a Hosting deploy as being an "emergency" lever that will invalidate the whole cache if you need it.
That being said, we are going to continue gathering feedback and usage patterns from developers making use of the new integration. If we can come up with an easy-to-use cache purging strategy that solves real problems developers are running into, we will of course consider that in the future.
In the meantime, I'd encourage you to play with the feature and TTL lengths to find something you're happy with.
Cheers,
Michael