You wouldn't unless you need to. (Does it fix a specific problem you have or add a new feature you want? If not, I don't see why you'd bother.) Some Z-Wave manufacturers provide firmware updates you can apply to their products with third-party software, a PC, and a USB Z-Wave stick if you want to. I'm not aware of any Zigbee manufacturer that does.
Last I heard, I think Hubitat is open to adding this feature regardless but doesn't have a timeline (and it would still depend on cooperation from device manufacturers). If for some reason you still want to do this, I might suggest suggest keeping your ST hub if this is important to you. They support OTA updates for Zigbee devices, and I'm sure the resale value on that thing can't be that great anyway. You can move the device over and back if you really want to.
To further the point I made above: are you aware of any firmware updates that have been released for any these devices for the purpose of fixing a problem you'd experience if you didn't? The only firmware update I actually remember doing because it mattered was the from the first public release of the SmartThings Button, which was prone to sending duplicate events (all I've bought new in the last year or so have come already updated). I've updated a few Z-Wave devices for new features (thanks, Zooz!) but you can't do that on SmartThings, either, so there's no difference. In the vast majority of cases, this is a non-issue, in my opinion, not worth getting hung up over.
SmartThings has provided some firmware updates for third-party devices (the Zen Thermostat comes to mind). This is up to the manufacturer (and Samsung to accept, I guess). All Ecolink products I've used are Z-Wave, so, again, not supported. They have never provided firmware updates for Hue bulbs; only Philips has done that via the Hue Bridge (but again, are you aware of any reason you'd want to update the firmware on these? about a year or so they added the new default power-on state feature, but that's only available when you're using a Hue Bridge anyway--and I'd strongly recommend not pairing these directly to SmartThings or Hubitat for reasons that are well documented for most Zigbee bulbs).
Battery powered Zigbee devices act as end points on mesh. They do not serve as repeaters. Devices serving as repeaters needs to powered at all times. Most Zigbee bulbs (other than Sengled) work as repeaters and can cause severe problems with the mesh if they are switched off via cutting the power breaking the mesh because they are no longer repeating. The mesh will self-heal, but it takes time. Worthy reads:
The ONLY SmartThings SmartApp that has any chance of running locally on the ST v2/v3 hubs is the Smart Lighting SmartApp. As @Eric.C.Miller mentioned, all of the devices must also run locally as well for there to be any chance of local processing. This means absolutely ZERO custom code for SmartApps or Device Handlers. Custom code ALWAYS runs in the ST cloud.
So, if you can accomplish all of your home automations using the SmartThings Smart Lighting SmartApp, and all of your devices can run locally on the ST hub using ST provided drivers, then you might be OK. But, please realize that any lighting that requires Sunrise or Sunset as part of the automation will not run locally. Also, if your Internet is down (or the ST Cloud is down) and you reboot the ST Hub, nothing will run again until a cloud connection can be reestablished.
Also, the ST Mobile Phone App ALWAYS communicates to the ST Cloud. It never talks directly to the ST Hub. Thus, if the internet (or ST cloud servers) are down, the ST mobile app is useless (even if you are at home on the same network.)
These are many of the reasons that I moved from ST to Hubitat as soon as Hubitat was released in Jan/Feb 2018. It would be very hard for me to ever go back.
As for firmware updates of Zigbee/Z-Wave devices... I have never really needed to do so. It depends greatly on the devices you choose as to whether or not firmware upgrades are even offered. Stay with the mainstream devices and you'll be fine. You can also take a device over to a friend's house who has SmartThings to update firmware if really necessary (or even possible.)
You can move the device over and back if you really want to.
