I recently got this Logitech M590, Bluetooth, basically for my daily work and silence feature. Just now I tried pairing with my Shield Tv and whoa... It's whole new world.
The mouse has dedicated buttons for vertical scroll (near thumb) and horizontal scroll (scroll button tilt) out of the box.
Why this is great. I have a few streaming apps which don't support Android Tv . Having dedicated scrolling buttons. Mouse allows me to horizontal scroll through different strips. Same go for vertical scroll wherever the pointer is. This is really great because even Shield controller can't do this. Also, shield app was is not this intuitive in mouse mode. One more good option in mouse to have quick switch button to change between two screen. For example, your Computer and Android Tv.
If you use such apps get such multi-button mouse, normally categorized as gaming mouse with dedicated horizontal and vertical scrolls.
Official Link: https://www.logitech.com/en-in/product/m590-silent-wireless-mouse
Let me rephrase your title:
Logitech M590: Multi button mouse with dedicated horizontal and vertical scroll is amazing for apps that never were designed to run on Android TV
If you are using mostly apps that were designed for Android TV, having a mouse with scroll has no benefit. It's actually a drawback, because some Leanback elements needs selection. So you can't scroll a row while you don't select any of it's items.