. Though, like much of Hobbit wear, it does seem to clash with the technology level of the rest of the world in the TA, doesn't it?
On the one hand, you're right. The earliest reference I've seen for what we'd call a knapsack is quite late*.
On the other hand, Bilbo also has matches and a clock on his mantelpiece. The Shire is very much a thing all it's own.
Regardless, I think we've got tons of descriptions - and drawings by the Professor's own hand - to indicate back-worn packs of some kind are known in Middle Earth, regardless of their place in our own history. I'd not personally take that as license to go full 20th century canvas and leather rucksack, but we all have our own mental image.
edit... actually, come to think of it.
Do we ever see a reference to the strapping on - say - the packs the Dwarves are carrying into Mirkwood? We know they were bearing their baggage on their backs, but whether in (what we'd call knap/rucksacks), or packboards, or just bundles with a single hooked strap is as I recall ambiguous. I have a vague memory we talked about that like... five years ago now.
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*John Rees has a wonderful series of papers on the subject on academia.edu, and he's found one letter from the early stages of the American Revolutionary War where one person is saying to another (effectively) - "they use this thing like a saddlebag, but it's got two straps that go over the shoulders!!" The implication in context being that even the early RevWar envelope-style knapsacks were strange new things to the observers.
Prior to this time, single-strapped backs over one or both shoulders appears to be the rule.
Persona: Aerlinneth, Dúnedain of Amon Lendel c. TA 3010.