The problem with the old system was that playing against unarmoured targets became wack-a-mole simulator, every time your unit got shot you had to go to ground, I think GW removed it because they gave every unit the ability to split fire as much as they like. It bogs down the shooting phase when you have to split fire in fear of wasting shooting on a unit that becomes extremely tough after the use of going to ground, whether it costs CP or not. We already see this problem with Quantum Deflection (Necrons), Take Cover (Astra Militarum), Rotate Ion Shields (Knights), Lightning Fast Reflexes (Aeldari).
Having Terminators go to ground also isn't very cool, but it's something you'd be forced to do when faced with overwhelming firepower, then your opponent just stops shooting you after you've gone to ground with your Terminators and they become sitting ducks for next round. Because going to ground isn't very heroic and Terminator like Terminator's didn't have the option in previous editions from what I remember, but then you have the problem of having to specify exactly what units can and cannot do it. It's easier to just not have it or just have the existing Stratagem for Astra Militarum.
I don't really want to go to ground with my Necrons either, I don't really love the changes to AP and cover this edition either. I think if you wanted to make a rule or Stratagem or something for this it would have to be for units with weak armour, like giving a unit a minimum save of 5+ regardless of modifiers or just giving the unit a flat 4+ sv. But again AM already have that Stratagem, it just doesn't come with the downsides you suggested.
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