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?

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.

Once EAD is issued, they can work.

Also the L2 holder has to apply for an EAD, which takes 4-6 months.

Many of them but not all. H4 EAD is for spouses of 1140 approved or 6+ years on H1 and green card process started.

That's right H4 EAD is a benefit of green card process and not just the H1b itself. However, L2 EAD is purely based on L1 and has no bearing on the GC process.