The more you can understand the fish's thinking the better, and every time you go out you learn a little more.
A spawned out beat up male steelhead in June is likely just waiting to die. They're not all repeat spawners - I think most of them only spawn once.
Unlike salmon, steelhead continue to feed, unless they are in really bad shape, like perched in a shallow bank, facing the wrong direction, swimming on an angle, etc.
If it's not showing any of the aforementioned signs of serious fatigue, it will still be far less keen to feed than it was in April or May. Your presentation needs to be near perfect. At dawn or dusk is probably best.
In late May, one of my favourite things to do is to drop a worm in a pool just as it's starting to rain. The rain drops create some cover for me, and most of the time this will produce a steelhead with only one drift. You can do the same thing in the middle of a rainfall or after, though you may get soaked.
For late spring steelhead, sometimes I will drift worms into a pool for 2-3 hours before one of them finally takes it, other times they take it almost immediately. They are not actively feeding this late into the season, so the onus is on you to entice a bite.
If you're fishing a popular area - most of those fish have been caught a few times already this season - which makes them even more fatigued.