Why cruisers were natural platforms for early missiles

Was the missile cruiser a new 1950s-60s idea, or did the concept appear earlier?

It emerged with practical missiles because cruisers had the necessary space at lower cost than battleships.

The missile-cruiser concept appeared alongside the idea of putting missiles aboard ships. Cruisers offered space for the new equipment and remained affordable enough to build. Battleships were a more expensive option whose future role was already in doubt. This makes hull space and cost the central reasons for choosing cruisers.