It is messy and overly ambitious, but promises something like a return to the "view source" mindset of the old web - where data was in plain sight and anyone curious and a little tenacious could reshape the web for their own needs.
I have gone partway down this path for a related concept, and browser extensions are really the only way to go. The biggest risk and hassle is a reliance on brittle, site-specific logic to make things work well. I haven't dug into this project yet to see how automated any of this is or might become, but if there is an element of community sourcing (like a ruleset for scraping AirBnB effectively) it opens up a potential attack vector like any GreaseMonkey-tyoe script, especially if passed routinely to less technical users. Not a huge issue on day 1 but not an easily solvable issue.