Yes, sharing with "partners" is certainly an issue - but I would posit that falls into once again, do you trust those companies.
There are companies I flat out to do not trust - Sony, Lenovo etc. They will need to work hard to re-gain that trust.
There are companies I have my misgivings about - e.g. LinkedIn (they are quite spammy), and I am very careful with what I share with them.
Then there are those companies that I use day-to-day, that I do trust - they provide a useful service, they haven't breached their trust, they have a good security track-record, and for me, the cost/benefits mean it's simply not worth the additional mental bandwidth of scrutinising everything single packet that leaves their app.
Examples - Github - I trust Github. Or say the HN forums etc. =).
I believe another poster here mentioned their IndieGoGo project - https://cloudfleet.io/#/ - basically 450 EUR for an appliance that provides email, calendar and file-sync - or the code is open-source.
With regards to the bank, I don't have a good answer for that - I live in Australia though, so the story may be a bit different there. I have had people (who indicated they were associated with my credit card company) try to sell me things - but I think that was just another division of my bank, as opposed to partners.
Finally - I agree with you, setting up your own Gmail-equivalent is certainly not trivial. The spam issue you mentioned is certainly one thing - for most people, they just want email that is reliably delivered - and also for incoming spam to be correctly marked as spam. Both of those are significant engineering efforts, in two vastly divergent fields (e.g. keeping up with all the standards like DKIM, SPIF etc. among other operational/administrative things, and machine-learning and large-scale data analysis). I would posit most people here are hardly experts in one, let along both (among all the other things they'd need to be experts in). That, and most people wouldn't have a large enough corpus to train the spam filter on anyhow.
Or say Github - yes, you could certainly setup your own Git repository - but say you hosted a project the PRC didn't like, and they wanted to DoS it - do you really think you could stand up to them, like Github has? There is once again, significant engineering effort involved here, infrastructure, backend, operational etc. in order to mitigate these things:
Eg. https://github.com/blog/1981-large-scale-ddos-attack-on-gith...
Most people simply don't have the know-how or time to execute those well (I wouldn't even try) - yes, if there was an open-source project that had the same backing as Github, the same number of engineers constantly working on it, and the same number of SREs/ops people making sure it ran well (or we had our own personal army of SRE/ops people...haha), I'm sure many of us would use it - but there isn't, and I suspect there won't be. Large scale turn-key web-apps aren't really where open-source shines.