That's a really good question; I'm keen to have Indigo support this scenario in the best possible way, but right now it has obvious room for improvement. In that light I'm interested to hear your thoughts on how it could support this better, particularly on a technical level.
I think there are two underlying issues:
Default config
At present the default configuration is to only respond to incoming traffic originating from 127.0.0.1 ie localhost. This is for security reasons, and I would not want to change that default (you really don't want your in-progress dev work accessible remotely by default, even traffic from the same network). However, I think there should be a checkbox or such that enables remote network access, perhaps for a set amount of time.
For now I think we need a documentation page describing how to override this config.
Name resolution
This one is trickier; some projects are probably fine being accessed by https://ip:port which (subject to the above config issue) makes them easy to access from a mobile device. However many projects (eg Drupal multisites) require name resolution.
The projects I personally work on with Indigo have multiple backends communicating with each other by their domain names and won't work unless the DNS resolves. In other words I have something like mysite1.test, mysite2.test and mysite3.test all communicating between each other. If I define mysite1.test in Indigo, I want that accessible not just on my Mac but on other devices on the network for testing eg mobile devices. Right now the best solution looks like systems such as Ngrok, FRP and the like, which would allow something like mysite1.indigoproxy.net. The downside being that sites will have to respond on two domain names (both mysite1.test and mysite1.indigoproxy.net in this example).
Thinking out loud here, and it's late, so I'm sorry if the above is incoherent!