I can't take credit for this because someone else highlighted this point in another thread, but one benefit of a smart EVSE that's been cited is that it would allow you to keep your car set to "Charge immediately" since you could use your EVSE to manage charge timing to take advantage of time-of-use rates.
This could be particularly useful if you use public chargers with any frequency, as you wouldn't have to remember to manually over-ride your in-car charge settings every time you use a charger away from home. I've seen a couple of people note that they had plugged in at a public EVSE and, on returning some time later, found that their car hadn't initiated charging because it was set to charge only within a specific time window. But, if you don't expect to ever use public chargers, this wouldn't be an issue.
Sidenote: One potential downside of using a smart EVSE to manage time-of-use rate charging is that things could get complicated if you also want to use the Mini's pre-set departure time feature. In other words, what happens if I set a departure time in the car/app that's outside of the charge window set via my EVSE? My assumption is that the car would go ahead and pre-condition for departure using its high-voltage battery since it wouldn't have access to mains power outside of the charge window, but, if anyone has experience with this, I'd love to know what actually happens (I do have a smart EVSE, but I've only had my SE for a week and haven't had a chance to test this).
One other reason a person might opt for a smart EVSE is to take advantage of rebates offered by some municipalities for smart chargers that are demand-response-enabled. For example, here in the States, my state of Oregon offered a rebate of up to $500 towards the purchase of a qualifying smart, level-2 EVSE. I wouldn't be surprised if, down the road, some utilities also offer ongoing rate rebates for customers with qualifying smart EVSEs who opt-in to demand-response programs. Our local utility here in Oregon already offers ongoing rebates for homeowners with smart thermostats who opt-in to their demand-response program, and extending this to EVSEs seems likely. But this is very much municipality/utility dependent and may not be relevant where you are.
One last reason I could think of to go for a smart EVSE is if you have multiple electric cars and want to be able to charge them simultaneously without installing additional electrical circuits. A smart EVSE with load sharing would allow you to "daisy chain" multiple EVSEs and would manage power delivery across each of those EVSEs to minimize charge time for each of your vehicles, while staying within the max load of your one circuit. One example of an EVSE with this feature is Tesla's Gen 3 Wall Connector, and I believe JuiceBox offers at least one model that offers load sharing as well.
Those are the potential reasons for a smart EVSE that come to mind for me, but I'm still very much a newbie to this world, so it'll be great to see the responses from folks with more experiences with EVs.