Does this need to say all this, or can it just say "Spells that spell's controller cast cost more to cast this turn?" Or "Spells the countered spell's controller casts cost more to casts this turn?"

You could compress the second sentence down to "Spells that spell's controller cast cost more to cast this turn." That'd be a minor change when used on things like Urza's Rage, but worth it for the reduction in text.

Well, this is now significantly worse than Render Silent.

Huh. Isn't it.

Yeah, I guess given Hindering Light this could go down to just costing .