I'd say the main thing to consider about an SR weapon is whether or not it'd open up a new option for you. That is, would it enable you to use a particular heroic soul you rely on in an element that you couldn't before?

For example, let's say Arthur and fire. Arthur needs a sword or an axe. You can't pick up a fire sword or axe through raid. None of the event SSR fire weapons are swords or axes. There are actually a few event SR fire axes down the road, but the nearest one is still a few months away, with fortunately just one wind event before then. If you haven't gotten an SR/SSR fire sword/axe from elsewhere and you're interested in using Arthur, the SR fire sword here is something to consider with the lower materials.

Or Andromeda and wind. No wind lance/staff from raid. I passed on the SR lance from Garuda. Then I realized that I wouldn't even be able go wind with the Andromeda line of souls for the two thunder events before the next wind event. I did get lucky and recently rolled Boreas from the gem gacha, as Boreas comes from a R wind staff. So my decision to pass earlier on stings less now. But I'll still need to pick up the next event SR wind lance, even if it has that +hp skill instead of assault.

Secondary reason is a quick SR level assault filler for the weapon grid, unless you've already got enough to push it out.

Still low priority, but it's basically only contesting some of the second round of soul points for the lower materials by the end of an event.