A document created by (or uniquely openable by) LibreOffice should show a preview of first page as its icon. That is what a modern more native app, like Apple's own Pages, does. At least current versions, on macOS Sierra.
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User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10_12) AppleWebKit/602.1.50 (KHTML, like Gecko) Version/10.0 Safari/602.1.50
Definitely nice to have.