They did handle the growth from search to email to integrated suite fantastically. And the lack of a broadly adopted ecoystem to integrate into seems to be the major stopping point for emergent challengers, e.g. Zoom.
Maybe the new paradigm is that you have your flashy product, and it goes without saying that it's stapled on to a tightly integrated suite of email, calendar, drive, chat etc. It may be more plausible for OpenAI to do its version of that than to integrate into other ecosystems on terms set by their counterparts.
However, I take your point - OpenAI has an interest in some other party paying them a fuckton of money for those tokens and then publicly crediting OpenAI and asserting the tokens would have been worth it at ten fucktons of money. And also, of course, in having that other party take on the risk that infinity fucktons of money worth of OpenAI tokens is not enough to make a gmail.
So they would really need to believe in the strategic necessity (and feasibility) of making their own gmail to go ahead with it.
In that case, there's some ancillary value in being able to claim "look, we needed a gmail and ChatGPT made one for us - what do YOU need that ChatGPT can make for YOU?"
Even at our small scale I wouldn’t want to be locked out of something.
Then again there’s also the sign in with google type stuff that keeps us further locked in.
The challenge in migrating email isn't that you have to move the existing email messages; any standard email client will download them all for you. The challenge is that there are thousands of external people and systems pointing to your email address.
Your LLMs memory is roughly analogous to the existing email messages. It's not stored in the contacts of hundreds of friends and acquaintances, or used to log in to each of a thousand different services. It's all contained in a single system, just like your email messages are.
Hide the notifications from uber which are just adverts and leave the one from your friend sending you a message on the lock screen.
Gmail already does filter the noise through "Categories" (Social, Updates, Forums, Promotions). I've turned them off as I'm pretty good about unsubscribing from junk and don't get a ton of email. However, they could place an alert at the top of your inbox to your "daily report" or whatever. Just as they have started to put an alert on incoming deliveries (ex. Amazon orders). You can then just dismiss it, so perhaps it's not an email so much as a "message" or something.