Making my conlang, I've found myself avoiding word-final stops (specifically p, t, and k) because I think they would be inaudible anyway. But does this phenomenon occur in all natural languages? Is this just a common trait, or is it actually impossible for humans to pronounce a plosive at the end of a word? I think Finnish marks plurals with a final t, but do they actually pronounce it or are they relying on some kind of redundancy, like how English speakers tend to pronounce vowels longer when they appear before a voiced consonant (or a voiced plosive, at least)?
"Is it actually impossible for humans to pronounce a plosive at the end of a word?" No, not at all. In French, word final plosives often have audible release (I just say "often" because I only have an intermediate level of proficiency and don't want to make too absolute claims; this may be understating things). I'm talking about words that end with a consonant in the phonology, not in the spelling. E.g. the word "tape" in French is generally pronounced [tap] with one syllable ending in a released /p/. A disyllabic pronunciation [ˈtapə] exists, but is not usual except for in poetry/singing or in southern France, so I usually see it transcribed phonologically as /tap/ (although it seems that some more abstract analyses of modern French make use of the idea of some kind of underlying final schwa in words like this).
Also, there is a difference between "no audible release" and "not pronounced". A plosive with no audible release is pronounced: the articulators make contact in the same place as for an audibly released stop. As you mentioned, the plosive is likely to affect the pronunciation of the preceding segment(s), allowing a listener to identify the place of articulation of the plosive.
This is somewhat like how some languages have geminate stops at the start or end of a word, even though gemination is not always audible in these positions (I am thinking of Swiss German in particular).