here we go again....
as has been said...we've discussed this before...
I would have to strongly disagree with you

I will accept the "not necessarily" because nothing is absolute... and exceptions or variations are always welcomed..
but to say most (if I'm reading you right) lyrics don't have a structured meter.... well those aren't the lyrics I ever choose to set to music.

After several years of writing complete songs by myself (25-30 years, I think... ) I have done several co-writes with lyricists here. And some of the best lyrics I chose had very strong meters.. some often almost wrote the music just by the lilt of the phrases. (and I know for a fact that the lyricist of some of those did NOT play an instrument)
If there isn't much structure in the lyric, then you run into the second verse dilemmas.... where the music that you have for the first verse does not mesh with the second... (and my personal biggest pet peeve where you end up singing a word with the accent on the wrong syllable because of the melody UGH!)
yes, playing an instrument and knowing some theory would not hurt a lyricist... as also..it would not hurt a composer to study some poetry, or prose....
but... we all have our strengths...
I know that by putting music to some of the lyrics I found from writers here, my music went in directions it probably would have not gone by my own guidance.