If I can miss subtle and not-so-subtle bugs in my own team's code that I'm working on every single day, what are the chances I'll get it right on somebody else's project?

Being able to MITM any HTTPS request on my system is a privilege I'd not grant lightly. It's up there with browsers, browser extensions (with "all content on all sites" access), and password managers in terms of blast radius in case anything goes wrong.