A global-presence ship with wartime value

Would Tiger Cubs be worthwhile only if they were markedly cheaper, fast enough to evade battlecruisers, and adequately protected?

Those qualities matter, but their decisive advantage is a peacetime station and global-presence role that does not require detaching a full battlecruiser.

Cost, speed, and protection matter when comparing Tiger Cubs with additional battlecruisers, but the two types are intended for different work. Tiger Cubs reinforce cruiser or battlecruiser forces in war while serving as the more routine face of British power overseas in peace. That global-presence role lets the Royal Navy keep expensive battlecruisers concentrated for the North Sea. Britain would still have a visible and credible intermediate deterrent abroad.