I've been playing guitar on and off for 9 years. I've gotten to the point where I'm happy with what I play when I do play. I can hear something in my head and play it for the most part (if it isn't too fast- yet even if it is, the rhythm makes it work).

The problem is all I do when I pick up a guitar is express my soul for about 3-5 minutes of improvisation. Anything else is just me wanking to a Metallica song or something. I enjoy my improvs as they're an outlet for me but I can never remember them and really wouldn't want to play them twice (or more) as a song. If I play them when my feelings don't match when I made them it just doesn't feel right... which in turn ends with it sounding bad and forced. They usually consist of a few repeated phrases that get a bunch of different fills and feels.

Should I bother trying to write a song?

I've always wanted to be able to, but it's so fulfilling to just pick up a guitar for a couple minutes and express everything you couldn't put in to words or tell anyone.
“Science cannot solve the ultimate mystery of nature. And that is because, in the last analysis, we ourselves are part of nature and therefore part of the mystery that we are trying to solve.”

-Max Planck

Record your improvisations, play for like 30 minutes. listen to the recording, pick your favorite parts, make it into a song. PRESTO!
Jam band man. write songs with solos you can improvise on like bluegrass. just jam through the whole song roughly based on a chord progression. most fun improv imo
If you're okay with just improv and playing other people's songs (and a lot of people are, it's totally okay), then it may not be that important. On the other hand, if you find yourself really wanting to write a song... Well...

Do what inspires you. It may not be songwriting, or it may not even be the same thing all the time, but if it inspires you then take the inspiration while it's there.