The 15-25% of demand number is pretty similar to the number I've seen in multiple places. Furthermore, cars have an economic lifespan of approximately 20 years, so that increase in demand will take place over a couple of decades.

Furthermore, if you're smart about it, you charge the vehicle at times when the grid is oversupplied with electricity. This typically occurs between midnight and about 5-6am, and in areas with a lot of solar, during the middle of the day. This is already widely implemented, with utilities in many jurisdictions offering things like EV charging time-of-use tariffs, and customers with rooftop solar systems (which are much cheaper in, say, Australia, than they are in the USA) installing smart chargers which are configured to run when they have a surplus of electricity from their home solar systems. This will ensure that EVs are making use of the existing grid, rather than increasing peak demand and requiring new grid infrastructure.

Furthermore, "vehicle to grid" systems can allow EVs to feed electricity back into the grid at peak times (with their owners getting paid for this service).

Given all of the above, while EVs will contribute to an overall increase in demand for electricity, they will do so in such a way as to minimise the need for extra infrastructure, and they will do so slowly enough as to allow such infrastructure to be built.