Shamelessly plugging the Librem 5 [1] here, as this article demonstrates precisely why we need a privacy-focused, FOSS phone. While the carriers having access to some of this information would not be prevented on a carrier-based data plan (and I personally am not yet ready to switch to WiFi-only), using a non-proprietary Linux distro means much simpler VPN support (one year of free VPN is also one of the stretch goals!). It might also be possible to compartmentalize PII availability by using WiFi only with an external data hotspot (e.g. the ones sold by FreedomPop), perhaps in conjunction with a VPN.
With regards to setting it up on Android, that does alleviate this specific privacy concern, however it is still entrusting your OS to Google and our carrier, neither of which have the best track records in consumer information privacy. Android also has limited app access controls and frequently comes with carrier-required bloat/spyware.
FWIW, DO can still see who is connecting to your droplet and what your droplet is connecting to. That's probably fine for staying out of sight from your mobile carrier. But many of the top VPN hosts now explicitly offer "no logging" as part of their services, like Private Internet Access.
Don't forget that Android is open-source, open-source, non-backdoored versions of Android exist.
I used to set up my own VPN server. As I don't trust the firmware (that was trying to send the data to the manufacturer) I have implemented a whitelist-based proxy that would allow connecting only to approved sites. Pretty inconvenient to be honest because sites often pull content from many domains including numerous CDNs with long meaningless host names. A web version of Skype uses some 20 domains if I remember correctly.
[1] https://puri.sm/shop/librem-5/