[loco5niner]

I disagree. "Let's assume" leaves room for doubt, where "it is obvious" allows for none. I think most people who use these phrases are going for the latter.

[diminoten]

An assumption is a prior, which necessarily means it can't be challenged, as in there is zero doubt about it, in the given/specific conversation.

Also, as a smell, when you say "I think most people" you're often just trying to mask your own biases.