Batteries have a very important role in transitioning off fossil fuels.
They do not inherently lead to disaster, but to make the transition, lithium batteries in their current form are insufficient. Fortunately most people aren't intending to do stationary energy storage for the electric grid with lithium. For that, sulfur-aluminum or lead-antimony (liquid metal) batteries are better, alongside pumped hydro, thermal storage, liquefied air, power-to-gas, etc, etc.
As the number of battery-powered vehicles grows, recycling of lithium becomes important, and sodium ion batteries (already manufactured, but not en masse) will be needed because sodium is much more abundant.
The electric grid will have to adapt. On some days, vehicles might not draw power from the grid, but return it - to balance out a power plant that dropped offline, or help during peak demand.
Traveling less will help and optimizing life to be convenient with less travel will help - but I think one can safely discard the possibility that everything can be altered. Unless economic shortage prevents them, people will travel, but the environmental impact of this can be very different depending on how they do it. :)
So - it's a puzzle with many bottlenecks and many ways to circumvent them.