"Okay, 6+3/4 inches doubled, that's 12+6/4 inches. But 6/4 is 1+2/4 which is 1+1/2, so 13+1/2 inches, or 1ft 1+1/2in".
"Okay, 17.14cm doubled, that's 34.28cm".
Really, for you the first one is easier?
The imperial system emerged piecemeal as a series of domain-specific measurements, where each unit conveyed deeper meaning beyond rote volume, distance, etc. For example, an acre means much more than 43,560 feet squared. It means "roughly the amount of land that a pair of oxen can plow in a day". A nice domain-specific measurement that communicates something useful to the experts of that domain, in this case, plowmen, farmers, and lords of the manor.
With inches, an inch is about the length of your thumb. Imagine doing woodworking and measuring in thumbs - it's right there in front of you, easy to conceptualize and work with, an intuitive "bite-size" unit of measurement. Fractional centimeters aren't as intuitive to work with and conceptualize. 6+3/4 inches is a lot more workable than 17.14cm.
Your example is a prime one. I'm not used to measure things with my thumbs, so if you told me that something is ten thumbs wide, I'd have to think some time before I could make a mental picture of it, and an inaccurate one to boot. I'm used to measure things with centimeters, so I immediately know what 10 cm looks like.
> Fractional centimeters aren't as intuitive to work with and conceptualize.
To you they're not. To people used to it, they are.
Example: I mostly work with 3/4" thick material, which is a breeze to divide into 3 for 1/4" mortice and tenons. The equivalent 19mm in that respect is a bit trickier, though fortunately EU 3/4 lumber tends to be only 18mm thick.