If you don't consistently use Dante you'll save yourself $500 right out of the box by not making that a priority in the mixer. Even venues where you could connect via Dante will have analog ports as well. It's really only an issue if you are trying to select/mute discreet portions of an arena's array, or access and manage multiple remote sources. Yamaha uses Dante for it's stage box connections and remote I/O devices, so if FOH and stage sets are in your future that would be the reason to value Dante.
If home karaoke is your primary use then I'd recommend the Behringer XR12 or the Midas MR12. Both of these mixers are superior to the Touchmix, and much more compact and portable. They are very powerful and price is under $500 (new.) I've acquired them (used) for as little as $250. The engine is the same as software used on the M32 and X32 consoles, so it's an easy step up if you ever find yourself behind one of those larger boards at a church or school. If you like control surfaces you can even use them with a Behringer X-Touch, though the mixers are so sleek the software apps are all you ever really need.
An XR12 can have a quad set of wireless mics on 4 of the TRS line inputs, leaving the 4 XLR inputs available for other mics, and another 4 TRS line inputs for music or other sources. It has Main LR and 2 Aux outs on XLR, and the monitor section can also be configured and routed as 2 additional Aux outs using the headphone left & right TRS outputs.
For karaoke you have a complete effects rack, monitor sends and onboard recording directly to a USB stick or via AUX out. Compression, parametric, EQ etc. all in a small 2U rack size. Wireless connectivity to multiple devices, cabled network, or both at the same time.
I've used these for wedding ceremonies, hybrid meetings, corporate presentation, and more. The only thing missing is output delay. When I need delay speakers I just add a 1U dual delay (Symetrix 402) which gives me dual delay capability from a pass thru of the main, or a single Aux.
None of the MR or XR series mixers have matrixes, but neither does the Touchmix and perhaps not the Allen & Heath as well.