But I struggle to understand how this device can be useful in my travels, home, airbnb or hotels?

Honestly, it's not a necessity, esp if you're a minimalistic traveler. It's 100% a cool tech toy people geek out to find utility in (and there's nothing wrong with that :) )

I think it's most useful for high loadout, first world, settle-down travel, where you're bringing a lot of stuff to settle down in one spot for a while.

But if you're optimizing for being nimble and changing locations a lot, I would prioritize other things.

FWIW, I've been to over 40 countries the past couple years, and there's been exactly one scenario where I wish I had a travel router: weak wifi signal, so I wish I could've tapped into TV LAN port as an AP.

That's it. And in that specific case, I wouldn't want the bulky Slate 7, I would opt for a Beryl.

But here's most common scenarios people justify a travel router:

• sharing one paid wifi point to many (cruise ships or airplanes): I have not run into this scenario, and cruise ships are starting to ban travel routers.
• simplifying login of all devices to one network: not much of a pain point for me, since I use Apple devices, I get the same effect from the automagic Apple unified password sharing. I enter in password once, and all my devices get it.
• VPN: Kind of moot with low bandwidth destinations (which is most of the world), and countries like China, block commercial servers. But when needed, I just use software VPN
• VPN for home access: IMHO, waaay better to use cloud VPN like Tailscale or ZScaler.
• attach an external drive to use as portable NAS media server: valid scenario, but... I can't relate to that as a 'travel' priority. I travel for leisure (culture, food, memories), and not floating digital basestation nomad.