This is not a solution at all. The churn rate on drivers is probably too high with Uber/Lyft services (most drivers aren't full time and do this when they feel like it). This means while the EV adoption is under the cutoff (40%) in your case, no new drivers would be joining while lots of drivers who are already active drivers become inactive.
This means not only are Uber/Lyft not acquiring any drivers (or just signing up a tiny percentage that have EVs) while they lose a lot of their existing drivers.
It sounds like it would work -- there'd be plenty of time when only EV drivers would be allowed to drive (since the quota isn't met at that moment). This would create a lot of incentive for people to get EVs, so that they could drive for Uber whenever they wanted, rather than only occasionally.
These conditions would need to be imposed on taxis as well, for maximal effect. Grandfather in existing taxis, and then past a certain date, new taxis must be EVs.
You're asking low income workers to suddenly front the bill for an entirely new vehicle. This isn't going to happen. What will happen is the same thing that did to people with the affordable care act in the united states: it becomes a regressive tax they pay because the alternative is simply too expensive. Better to pay the tax penalty than an unaffordable insurance requirement per month.
Most rideshare vehicles are financed, not bought outright in cash. If the increase in income from driving an EV exceeds the additional monthly cost of an EV then it's a no-brainer, especially once you factor in cheaper fuel costs.
And your take on the ACA is quite off; it's given healthcare to many more people than previously had.
Is Lyft still arranging leases for drivers / do they do that in India? If so, that's an easy place to encourage EVs.
Guaranteeing and publicizing a better rev share for EVs could drive adoption, although slowly. For quicker adoption, they could set up a wait list for drivers with non-EVs and tell the drivers they can skip the line if they get an EV. For every two EV drivers that sign up, they can also let in three non-EV drivers. When a non-EV driver quits, they reduce their EV deficit; when an EV driver quits, their EV deficit increases.
This means not only are Uber/Lyft not acquiring any drivers (or just signing up a tiny percentage that have EVs) while they lose a lot of their existing drivers.