Bacon Bits
Legend
There's no such thing as a "move action" in 5E. Same issue applies with your Counterspell change. I see what you're getting at but the way movement works in 5E this potentially has ramifications beyond what you may be considering. It also leaves True Strike as still pretty bad.
You say that like it can't possibly work that way. The Aim action for Rogues from the Class Feature Variants UA already works that way:
Cunning Action: Aim
2nd-level rogue feature (enhances Cunning Action)
You gain an additional way to use your Cunning Action: carefully aiming your next attack. As a bonus action, you give yourself advantage on your next attack roll on the current turn. You can use this bonus action only if you haven’t moved during this turn, and after you use the bonus action, your speed is 0 until the end of the current turn.
And the grappled condition already uses similar language to prohibit movement.
Counterspell could easily say:
Counterspell said:You attempt to interrupt a creature in the process of Casting a Spell. If the creature is Casting a Spell of 3rd Level or lower, its spell fails and has no effect and you are incapacitated until the end of your next turn. If it is Casting a Spell of 4th Level or higher, make an ability check using your Spellcasting Ability. The DC equals 10 + the spell's level. On a success, the creature's spell fails and has no effect and you are incapacitated until the end of your next turn. On a failure, your move speed is reduced to 0 and you can't benefit from any bonus to speed until the end of your next turn.
Sure, it's super fiddley and I wouldn't play with the spell this way, but mechanically it works just fine. 5e is certainly capable of it. No, we don't really need to care about misty step or other oddball corner cases. This is D&D, not Magic: The Gathering.
Personally, I don't have much of a problem with counterspell. I would prefer that it didn't have the "At Higher Levels" clause at all, but that's really pretty minor. If I really have an issue with it interfering with my encounter as a DM, I would probably just add an additional spellcaster who has counterspell, but that's somewhat of a luxury of milestone leveling.
True strike I think is fairly useless, but it is useful in an ambush or when combined with a much higher level spell that requires a spell attack roll. In both of those cases, you can't really just attack two turns in a row. However, it's somewhat rare that you actually care that much, so its just not that useful. I think true strike would also be more appropriate if it cost a bonus action and then prevented you from casting spells and gave you disadvantage on attack rolls the next turn. However, I think that's too fiddley for 5e.
Blade ward has the same problem that true strike does. It's only useful when Dodge doesn't work because your attackers already have disadvantage. That just doesn't come up often enough.
Spare the dying I think is shockingly awful. When a Healer's Kit costs 5 gp for 10 de facto potions of spare the dying, and you can make a Medicine (Wisdom) check to do it instead, too, it's just inexcusably bad. Both of those take a standard action, and spare the dying is range touch. I think either the cantrip should either have a range (15 to 30 feet), should only require a bonus action, or should have some other benefit (e.g., automatically succeeds on death saves over a specified time period).