Grassmann's approach is not "klunky and difficult". It's clear and straightforward and makes proving some difficult results much easier than the previous method

Grassmann's approach is not "klunky and difficult". It's clear and straightforward and makes proving some difficult results much easier than the previous methods, it just takes a bit of a leap of faith to practice enough with it to build fluency. (The subject itself is also challenging, irrespective of approach. When you strip away some of the incidental complexity of a mismatched representation, the inherent complexity of the subject still must be contended with.) I'd recommend people try to directly read both of Grassmann's two books; there are translations of both into English. (Disclaimer: I haven't made it through either one beyond a skim and reading the first few chapters. Then I got distracted by some other project. Like any math books, reading them takes a lot of slow careful effort.) It's kind of like taking a bunch of people used to riding horses and handing them a bicycle. The bicycle is not "klunky and difficult" compared to the horse, it's just unfamiliar.