H4 dependents can only work after the primaries's green card process reached certain stage which may take few years.
But with L1, spouse can start work from day 1
Incorrect, the dependent has a 3 month waiting period.
you mean they become eligible only after 3 months?
Also the L2 holder has to apply for an EAD, which takes 4-6 months.
Yes, as the other comment says. They become eligible to apply for EAD only after 3 months. You then need to wait for the EAD, which processing time varies depending on location.