Currently, whenever you want a specific Assistant page and then use the dropdown to select your Assistant. It will default to the last used Assistant even across multiple devices. This means very often changing manually changing your assistant.
Allowing hyperlinking to specific assistants, both custom and default, would let you be able to quickly access a specific assistant via shortcut or url.
A few examples:
I have an assistant designed to provide concise and definitive answers when on a mobile device and I don't want to have to scroll or read a lot. Currently most of the time I open assistant via my iOS 'shortcut/installed app' it returns me to what I was last using on my PC and I have to change it. With a hyperlink my shortcut could take me directly to my 'Mobile Assistant' on my phone.
I have a shortcut in Firefox to go to Assistant. When I am doing a Code session or another specific assistant session its not a big deal to change the settings. But most of the time I want to access my preferred settings. This again could be accomplished via a hyperlink.
While a 'default' setting could be useful, the hyperlink option would go a step further allowing everyone to customize everything to their heart's content even across multiple devices.
Simple URL parameterization should work nicely for this using the assistant name and settings.
