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).
This paper mentions that French, Polish and German plosives are always produced with audible release.
There are languages which do not allow stops either word- or utterance-finally (e.g. Italian, Tamil, Japanese), while in some other languages that do allow final stops they are regularly produced with audible release, i.e. a kind of vestigial vowel (e.g. French, Polish, German).