So a couple of things. Z-Wave is a proprietary protocol (developed by a single company called Zensys) and is a closed ecosystem, so personally, I'm not a fan of it. And it's not great choice for interoperability either.

Zigbee on the other hand, is an open standard (IEEE 802.15.4), made by the Zigbee alliance, comprising of major tech companies. The Zigbee alliance later became the Connectivity Standards Alliance (CSA), who are the ones behind Matter. Which is why it appears as if Matter is trying to resolve Zigbee issues.

In actuality though, Matter is trying to proposition itself as a generic standard for the modern IoT world, because things have changed significantly since the times when the Zigbee and Z-Wave protocols were conceived (late 90s - early '00s). The main thing that's changed is that low-power and cheap system-on-a-chip (SOCs) and single board computers (SBCs) have taken over the world by storm, which has enabled manufacturers to push out cheap home automation products quickly. Making home automation products is no longer a traditional embedded systems and specialized electronics play, where you had to invest a lot of RnD into designing complex circuits, pay for a Z-Wave license etc. Nowadays, even a kid could make their own system using a Raspberry Pi and say Python, without needing any knowledge of low-level protocols or languages.

As a result, the home automation world is filled with too many manufacturers and products, all trying to do their own thing and in-effect, building several closed ecosystems, even though they're all basically using the same protocols behind the scenes. Plus you also have the existing Zigbee and Z-Wave products.

So before Matter came into the picture, several manufacturers started making their own centralized hubs, as a means for interoperability, like Samsung's SmartThings, or Apple's HomeKit etc. Some even have their own closed hubs meant for their own ecosystem of devices, like the Philips Hue bridge. As a result, some homes may even have multiple hubs, with overlapping functionality.

Matter aims to unify all of that. So instead of Philips doing their own thing, instead of Samsung coaxing manufactures to make their systems compatible with SmartThings, instead of manufacturers kissing Apple's ass to support their products, instead of x company making some half-baked bridging app for y company because the specs haven't been fully documented or they simply don't care.. we have Matter. Matter aims to solve that mess, at least, on paper. It would still require manufacturers to actually buy into the idea and support the protocol, but at least it's better than working individually with Samsung and Apple and Amazon etc, or reinventing the wheel and doing their own thing.