We can all guess here as to IF those parts are REALLY bad but if what they're saying is true, then they should be able to show you the worn parts on the car before you OK their replacement.
I've been a tech for a very long time and I can back up anything I say that's bad about any car I see. Anytime a customer might have any doubts, if they want I'll be happy to show them the worn parts, what I'm seeing and prove beyond any doubt that what I'm saying is true. Any good tech doesn't need to make up BS and lie as there's plenty of real work that needs to be done.
I won't comment about the total price as I don't know what their labor rate is or what labor guide they used to quote the price. I do know that our dealer sells those control arms for about $180 each now.
If in doubt, ask to have the tech show you what he's seeing. If he's being honest (which he should be) then he should have no problems in showing you the worn parts.
Control arms (w ball joints) in themselves don't require an alignment when replaced but if any tie rod end is changed, the car needs an alignment. If you have loose/worn parts, they can't align the car properly.