This is old, but shows the Now setting for stocks[0].
[0] https://android.stackexchange.com/questions/41357/how-do-i-r...
In other contexts "Google does not forget" means what can be found through web search, but here the grandparent was using a broader meaning, closer to "once shared, data is no longer yours".
This Whac-A-Mole is not a game, and that will not end well.
Either way, anecdotal cases like this don't really support or refute your claim.
A long time ago, it was possible to remove Google products and services on a case by case basis.
There were public URL from which you could request the deletion of your data. You could find it at http://ruscoe.net/google/google-account-service-names/ ("Google Account Service Names" link, which now redirects to some notice about the blogger's life). The list was crowdsourced by Blogoscoped's members and maintained by Tony Ruscoe (who made the list unaccessible right after being hired by Google).
You can find some in these "EditUserServiceData" URLs on this post: http://blog.ruscoe.net/2006/06/google-rs2-ssd-and-mobile-dow...
Times have changed a lot (for the worst) since 2008...
I thoroughly and repeatedly deleted all stock-related information from my Google account: all portfolios removed, all search history erased, all past Google Now topics suppressed, past emails deleted, Google chat conversations removed. Just everything (and I know really well how to control data on a Google account, I was once a Google fanboy and explored every little feature I could get my hand on, so customizing my Google account/products settings is something I'm quite good at).
Guess what? Going to their new google.com/finance brought all the stocks I've once added to Google Finance and removed. More than a dozen of stock tickers were automatically added to my account, and listed as "following".
It's impossible for me to completely delete my Google account because of some work-related obligations, but Google just proved that it will NEVER allow you to get forgotten.
We're forced to feed a beast we can no longer escape.
PS: the only Google things I occasionally use now are Gmail & Google Contacts (planning to switch to ProtonMail, but waiting for a contact syncing service on Android) and search (when Qwant isn't good enough).