Oh yes, that account switching thing is a pain... Their login page also redirects you a couple of times whenever signing in but I guess that's fine - it has to work with whatever custom security stuff Office365 customers have set on their instances. I just wish it felt less like a kludge.
If a witch approached me and told me she could make Microsoft Teams disappear for good at the cost of severing a finger (presumably for a potion...I've got no idea; I'm a developer, not a witch), I'd offer her two for the trouble.