You're actually onto something — summoned creatures DO tend to hog kills, and it feels way less satisfying when you're just standing back watching. But nah, don't ditch conjuration entirely. There's a middle ground that works really well.
The key is the Conjuration perks that don't rely on summoning dudes. Soul Trap is exactly what you mentioned, and it's genuinely strong with melee because you can trap souls while you're actively fighting. Pair that with a sword-and-board setup and you're constantly feeding grand soul gems while you're doing your own damage. The perk that lets you trap souls on hit (instead of needing to wait for death) makes this way better.
For actual summoning, there's a perk that boosts your summons' health and makes them tougher - so instead of them dying instantly and you needing to keep recasting, they tank hits while you wail on enemies. That feels more like they're your companion than your replacement. Summon them, let them grab aggro, then you move in with your sword. It's a different rhythm than pure melee but you're still actively playing.
Honestly though, if you really want to feel like you're doing the work, the Atronach summons (especially on Master or Legendary difficulty) are less obnoxious about kill-stealing than Dremora Lords. They hit hard but they're not smart enough to rush every kill.
What difficulty are you playing on? That changes how much the summon actually matters.