Your use case is very reasonable, and a lot of people want it. But it's a big challenge from a technical/engineering standpoint. You know how a replacement battery pack for an EV costs like $8k and has a range of 300 miles? Your rental battery would cost at least that much, plus whatever costs are involved to make it portable, and integrate it's usage into your existing EV. Then the rental places would need to have massive charging capabilities for when people stop in to swap their empty rental battery for a full one, since it still only has a range of 300 miles (4-5 hours of freeway driving)

I actually think there will be improvements on the fast charging front. You can already see this idea in other places. Many heavy duty trucks have 2 fuel tanks. You can fill them with 2 standard pumps running simultaneously, effectively giving you double the refueling speed. Some phones have dual batteries for the same reason.