Every method of visualisation has its strengths and pitfalls. One of the pitfalls of this method is that it always looks rather dramatic, regardless of the data. Changing the shape of well-known things gives an uneasy feeling, regardless of what you map.
Only data that is perfectly equal will not result in arbitrary distortions. The amount of distortion, magnitude of the local scale factor, is (or should be) a parameter of the visualisation, just like the decision of using a fiery red-yellow colour gradient.
Linked source has a bit more info on what exactly they did. Which is simply substituting area for value in dollars. Only makes sense if the data somewhat follows a normal distribution. And I'm going to guess here, property value does not, at all. It's not even bounded. I'd have picked log value, because an exponential distribution for the value is a much more reasonable assumption.
In case of a visualisation like this, I might actually decide to do something that is generally frowned upon: change the "origin" of the data. That is, add some constant value to the scale factors, to smooth out the severity of the distortions a little. If I were mapping the log value that wouldn't be necessary since it'd be equivalent to scaling dollar values to $1000 or $1M, etc.
I'm trying to remember other examples where data was mapped to local scale in a non-shape preserving way.
The only thing I can come up with was a sort of homunculus visualisation (I forget if it was just a drawing or actually made into a 3d clay statuette). It scaled our body parts roughly proportional to the volume of our brain dedicated to it. So you'd get a giant head with huge bulging eyes, etc. It looked weird, funny, still somewhat human/cartoonish. It showed things as "this is MUCH bigger than that" or "huh I didn't realise my tongue was that important". It wasn't a very clear visualisation, but I'm also hard pressed to come up with a better way to do it.
In other words, this type of visualisation helps to show the data in a mostly qualitative way, not quantitative. And like the homunculus example, the data doesn't need to be super exact (we can't estimate relative area/volume of irregular shapes very well).
But it looks cool.
