I agree in theory, but you're never completely in control of what's running on Android because there are still proprietary bits (like device firmware) that we can't replace, right?

That argument is moot, even if you use a device that's 100% FOSS and you actually have total control over even down to firmware, like a Raspberry Pi cyberdeck/small form factor PC you built yourself using open source wifi cards, you are still connected to an internet infrastructure that's filled with proprietary devices such as routers and servers which you have practically no control over, and deliberate malicious actors can still do MITM attack for example as long as any data is being transmitted. And it's not really a personal mobile device anymore if you don't connect it to the Internet at all.

However, even if you cannot ensure 100% control, having root access on your personal device enables you far greater freedom to monitor and investigate the behavior of the proprietary stuff you can't control directly, and mitigate or bypass the security and privacy vulnerabilities they might poss with far more options than is ever even close to possible on an unrooted device.

For example, there are many apps I need to use because of services I need to use because of the city I live in, they have known track records of security and privacy violations. With a rooted device I have the freedom to capture every single pocket they transmit and analyze on Wireshark to see what they are doing, I can block internet access specifically for these apps without conflicting with my existing VPN setup, I can spoof my device's IMEI and other identifiable information for specifically these apps so they can't identify my phone, including even spoof my geolocation without the apps realizing they are spoofed, I can block these app's access to my phone's application list so they can't profile me by seeing what other apps I have, I can block their access to my phone's sensors without the apps knowing they are blocked (other than getting empty sensor reading), I can even deny permissions to those apps without the apps knowing the permissions were denied. On an unrooted device you either need ADB or can't do any of these at all.

Also, without any of these tools how do you even know your device's manufecturer has done everything they need to do to protect your security and privacy? Just because they said "Trust me bro!"?

Principle of least privilege is completely irrelevant here, any system app provided by your phone's manufecturer already have total system control anyway, including Google's GMS apps and Facebook framework apps that are pre-installed, and without root you also do not have an option for truly stopping or removing those apps.