Seventeen-hundreds doesn't sound stilted at all, to this native English speaker. I would use this even in a very formal context, and certainly no one would bat an eye. One-thousand-seven-hundreds is almost certainly incorrect in English -- I would actually find this to be a very clear marker of not speaking English very well. Are you a native speaker? I find your claims rather bold and quite frankly incorrect.
Also, curious to find out (from elsewhere in this thread) is that Finnish does not typically use centuries. Rather, they use a construction that maps directly to 1700s (1700-luku). I would be careful in accidentally applying your own cultural bias when accusing others of the same ;)
In Swedish it's also very rare to count centuries. We say 1700-talet. Also 2000-talet (pronounced either tvåtusen-talet/twothousand-talet or tjugohundra-talet/twentyhundred-talet) would mainly refer to 2000-2100. To refer to 2000-2009 we say 00-talet (nollnoll-talet/zerozero-talet).
Also, curious to find out (from elsewhere in this thread) is that Finnish does not typically use centuries. Rather, they use a construction that maps directly to 1700s (1700-luku). I would be careful in accidentally applying your own cultural bias when accusing others of the same ;)