I think there's also some confusion here, as there often is with Matter: the hub functioning as a Matter bridge compared to the ability of (other) Matter bridge devices being able to be added to Hubitat.
The former is not supported and is not what most hub manufacturers mean when they say that they "support" Matter -- unless it's a special-purpose device like the Philips Hue Bridge, SwitchBot Hub, or similar, where is a way to bridge the devices' native to protocols to Matter (but doesn't mean can add Matter devices to those systems).
The latter technically is supported on Hubitat, but, like any device, you need a driver that will work. Matter might make this easier, if anything, but support is still relatively new and there are no built-in drivers at the moment for anything that happens to be a Matter Bridge--but that's not a technical limitation.
Again, a standard that is not standard. For me, a device with a Matter label should be able to be driven by any hub that talks Matter (not talking about the connection where Thread is recommanded by Matter but not mandatory) in the way it works now for supported non Matter devices (within the limit of the Matter functions in the standard). In contrast, a hub with a Matter label should be able to drive any Matter device AND be a fully featured member of a Matter network. So Hubitat should be able to connect to a Bosch Matter Hub and to drive Bosch devices exposed as Matter devices.
If that does not work, the Matter label is worth nothing. Maybe the label is not well done, as it should show 1.0 or 1.3 for example to know the compatibility with a version of Matter. As everything should be downwards compatible this would be a good information to know.
Matter is just a confusing mess, designed seemingly from the ground up to be difficult to understand. Comments like above show the confusion its design can cause. In the end the Matter alliance (or whatever its called) decides who can call themselves a Matter device/hub/bridge, etc., so any blame for confusion related to that falls back on the Matter group, not HE.
Let's apply that logic to Zigbee & Z-Wave certifications as well, to be fair. So if there is a single Zigbee or Z-Wave device that HE (or any other Zigbee/Z-Wave hub, like Home Assistant, SmartThings, Tuya, Aqara...) doesn't have native drivers to support, those hubs also cannot be identified as a Zigbee or Z-Wave hub and use those logos? That logic would essentially de-certify every Zigbee and Z-Wave hub that exists.
You’re not the first person to notice that Matter’s rollout in the real world has come with various caveats, footnotes etc. that don’t lend themselves particularly well to a simple logo as a marker of “support” for the underlying framework.
But that’s not something Hubitat has much control over.
And also not realistic, IMHO -- there is no reason for every Matter bridge to also be a Matter controller and vice versa, and either raises additional concerns (in particular, Matter bridges are generally designed to work with only specific devices, otherwise you're stuck with a "driver"-type problem for getting arbitrary devices out and the same question for getting them in, plus if or how you might be able to use them in that system -- what would a Hue Bridge and the Hue app do with a thermostat?).
I do not agree. Nearly every device (and Zigbee TRV) that follows the Zigbee standard can be connected to Hubitat, but not controlled or polled as a device specific driver is needed. Matter in contrast requires a unique internal driver for a TRV for example that understands the standard Matter commands for this type of device. Every Matter compatible TRV understands and speaks this universal language and can be controlled and polled. The Hubitat stuff only has to create this brand independent Matter driver and every TRV exposed by a Matter hub (or controller) should work.
The staff to do by Hubitat is the ability to see exposed devices and native devices and to create one driver for every device type in the Matter Standard. That's Matter! It's simple. That does not mean that it's not hard work to implement it, but the design brief is simple and clear.
Yes, and no. Matter bridges are designed to work exactly the same way they work but with Matter on a second layer. So IMHO a Hue hub will just expose Lights and connected staff and also just be able to control this type of staff as this is what it also does without Matter.
Hubitat is a fully featured smart home hub (at least they say that it is), that can control heating and TRV (it features a native driver for the Spirit TRV and a generic driver - that never works), so it should also feature a Matter TRV driver that by design should work with every Matter TRV or TRV exposed as Matter device by another Matter hub.
As much as I like gadgets and over-complicating most things in my life, starting with espresso in the morning, the multiple caveats for Matter have made me completely disinterested so far.
When I can use my Hubitat to "add device" for a Matter gadget in the same way that I do for Zigbee and Zwave gadgets, then Matter devices are on my shopping list. And if there are respectable, well thought-out reasons why that is a stupid idea that can never happen, then I am just not using Matter, I guess.