How does Google get away with not ever supporting previous releases? Don't customers demand this?
That said, Google doesn't support previous releases for security reasons. We are constantly improving the security profile of Chrome, and hackers (both black hat and white hat) are constantly finding exploits in older versions. (The same is true for all the other major browsers on the market.)
If you want to use Chrome on a previous/older release, please don't. If you want to use Chromium on a previous/older release, also please don't, but you can compile it yourself if you're so inclined.
And for the most part, no, customers don't demand stable old releases of Chrome. They've learned how bad of a security and usability mistake that is from IE6, and they don't want to repeat past mistakes any more than we do.
I suspect that there are lots of enterprise customers that haven't learned that (encountered it, but not learned it), but they probably aren't Chrome customers, since they are still using IE.
If you instead view IT departments as the customer, then yes, they care and want to have control over the deployed version of the software on their networks. Chrome does have some controls for this. I'm not that familiar with them, though.
Kongregate currently tells you chrome broke Unity with its current version and you should use Firefox instead. If previous versions are not available, switching browsers is an alternative workaround.
Engineering is about tradeoffs. You can't implement everything someone might want. The desire to have the product continuously improve is in direct conflict with the desire to have the product never suddenly break.
In this case the team believed the positives dramatically outweigh the negatives and I agree. Continuous silent updates are one of the best features of Chrome. All consumer software should have it.
As a developer, I wouldn't recommend an old browser solely for security reasons, but also so I can stop support ancient browsers sooner…