Timeout trees can be used for lightning channels but it's not really their only use.

Lightning's biggest problem actually IS channel opens right now, it would take ~5.5 years to open 1 billion lightning channels right now. Whereas you could (in theory, but there are practical limits much lower) open 1 billion lightning channels in one transaction with CTV.

*Then* the problem becomes uncooperative closes (force closes and attempted thefts). If you have a billion people competing for block space to handle closes, that could get messy too.

But if we can use CTV to increase channel open capacity, and we can limit the need for uncooperative closes, then overall capacity dramatically increases.