Not really. They do gradually lose capacity over a long time, but it's a slow process. The US Government requires EV batteries to have an 8 year / 100,000 mile warranty, and California requires 10 years and 150,000 miles. I expect most batteries will significantly exceed that.
LFP batteries generally have about 3x the longevity of other lithium ion types.
There are some examples of early battery failures, like the Nissan Leaf didn't use liquid cooling; now basically everyone else learned from their example and does it. Chevy Bolts had a battery recall due to bad manufacturing. Basically, if a battery fails early someone somewhere screwed up. Most EV batteries are fine and will continue to be fine for a very long time.
>> "I’m not convinced it ever will be, especially if it’s continued to be made by exotic materials."
Resource constraints are an issue, but there are workarounds. Nickel and cobalt can be avoided simply by using LFP cells. Permanent magnet motors are more efficient than induction, but the permanent magnets don't need to be based on rare-earth elements -- it's just that the non-rare-earth-magnet version would be less powerful and/or bulkier. Similarly you could wind the motors with aluminum instead of copper, and the motor would be less powerful and/or bulkier. But that's fine -- electric motors are already quite a bit smaller and more powerful than they need to be anyways.
Lithium is probably the hardest-to-get-around resource constraint with current technology, but lithium production is ramping up.
Also worth noting that the need for large batteries would be substantially reduced if were to invest heavily into charging infrastructure and even the electrification of roads so that cars don't even need to stop. (There are some projects in Sweden and Germany along those lines.)