It's complicated. Matter over Thread is indeed nice in that it you only need generic Thread and Matter servers. It also makes it easier to share credentials between ecosystems. Thread itself is also a pretty nice standard technically.

There are also strong downsides though, one is privacy and future cloud lock-in. Zigbee is fully local. Previous Thread standards added the option for NAT64 so that Thread devices can access the internet and there were some Thread + Matter devices that already require internet access for full functionality (IIRC some Nuki smart locks, but I might misremember). However, Thread 1.4 also adds support for Thread devices to get a globally routable IPv6 address. The Thread 1.4 whitepaper is pretty blunt about what this enables:

Simplified Cloud Integration: Thread devices can now seamlessly connect directly to cloud services, enabling remote control, monitoring, and over-the-air firmware updates.

https://www.threadgroup.org/Portals/0/Documents/Thread_1.4_F...

The fact that Thread and Matter are strongly pushed by Google, Apple, etc. should tell you enough.

Now, a TBR may simply allow you to disable NAT64 or globally routable IPv6 addresses (e.g. Home Assistant's addons), but many consumer implementations don't. E.g. the Apple TV is a Thread Border Router and does not allow disabling NAT64, so Thread devices can access the internet, send analytics, and can be cloud-controlled.

Also, the ecosystem is still pretty immature, as a result of which you can encounter issues, typically resulting in unstable device connectivity. E.g. TREL does often does not work well. Apple has some hacks to fix most of the issues, but it only works well between Apple devices. So it's generally the best to avoid combining multiple TBRs into the same network.