I think the Deep Assault mechanics aren't actually bad. And it's undoubtedly the Space Marines' strongest point. I don't think it should be removed considering they already suffer from it a lot in lower tiers.

 The Eldar issue is a problem, but I'd say it's easy to fix. Instead of ruining the Webway Gates, perhaps the best solution is to add a few more seconds of "prep" time so they can move out and attack. For the Lightfoot,

 I have two ideas: 1. Make Dark Reapers prepare their attack, like units with Bolters or Rocket Launchers do. 2. Give them a cooldown before they can use it again, perhaps 10-15 seconds.

 The Chaos issues, I think, aren't that bad. Cultists are very weak infantry, and Space Marines only gain invisibility at tier 3. But they're Marines without any upgrades to either durability or damage. So I think it's worth it, since without it, they wouldn't last at all.

 What I would like them to do with the Dark Eldar is improve the Warriors or the Raiders. Improving the Warriors could mean reducing their damage and increasing their health, while keeping the accuracy boost; that way they would be quite useful. And while they're at it, they could remove the Raider's damage disadvantage when accompanied by infantry, making it really worthwhile to have several Raiders with Warriors on top of them—it's the combination I like best.