So, I did some research, and although I never found anything that specifically said "This is why you shouldn't tool chrome-tanned leather," the information that I did find suggests a reason.
Lots of resources describe the difference between chrome- and vegetable-tanning. I think this quote (from the GoldBark Leather site) summarizes things pretty well:
There’s a lot that goes into each of these tanning processes. What’s important to know is that one uses vegetal oils (from tree bark) to tan and another uses chemicals (chromium) to tan it. Vegetal tanned leather, generally referred to as veg tan, takes a longer amount of time to create, is considered higher quality, and therefore costs more. Chrome tanned leather has a quicker turn around time and therefore costs less.
The end product of these two processes are drastically different. Veg tan is generally thicker, more firm, and more durable. It’s the kind of leather you see in a nice pair of leather shoes. Chrome tanned is thin, very stretchy, and less durable. It’s the kind of leather that you see in a car that has a leather interior.
The Carryology site also has some interesting information about the actual chemical processes and how they differ. It explains that in vegetable tanning, tannin molecules displace the water molecules that are bound into the collagen within the leather. In chrome-tanning, chrome molecules replace the water molecules within the collagen. It goes on to explain:
chrome ions displacing the water and binding with the collagen are much smaller than vegetable tanning molecules. This generally makes chrome tanned leather thinner and softer than vegetable tanned leather.
Because I don't know anything about tooling leather, I did some searching about that process, and ran across some good information on this forum posting. From the fourth entry:
You simply can't tool, carve, or stamp Latigo or oil softened leather
like you tried to use.
You need to start with Vegetable Tanned Tooling Leather. It's almost
white, and almost hard when you buy it.
Then wet it damp, but not soaking wet. Then wrap it in a towel and let
it set for an hour or so to 'case' it. That allows the moisture to
work through the leather fibers and prepare it for tooling.
Once it reaches damp, but not dry enough to turn light color again.
You can carve & stamp it to your hearts content. It takes tooling,
molding, and shaping around a gun almost like modeling clay!
Then once dry and oiled, it will retaing the stamping & shaping
Avoid belly and leg cuts as it is soft & stretchy and will not retain
Once I read this information, it seems obvious why chrome-tanned leather won't work well. Chrome-tanning reduces exactly those elements that make a piece of leather appropriate for tooling--thickness and stiffness.