The biggest risk is individual cells failing.
On vehicles like the Leaf this is easy enough to fix, the same applies to older Model S and most newer EVs. Newer Tesla's seem to use batteries that are glued together and are a lot more difficult to service.
Some older EVs have shorter battery lifespans than desirable, e.g. older Leaf's. Those are ones to avoid, though still ok for local journeys, road tripping in a degraded battery 24kWh Leaf would not be fun.
The battery pack on my PHEV is holding up well and it gets cycled brutally, the thing that worries me is more the gearbox, that judders now and then, which is a common issue on DSGs as the clutches recalibrate. You don't have automatic gearboxes on pure EVs. There's also the worry of the turbo dying. Strangely enough EV's don't have those either.