"Do people not see how hard they are making the lives of future developers (or even their own lives down the road) by continuing to coddle these people?
Your vet example would be happy to switch to a cheaper service (cheaper because the devs were cheaper, because the tech is more modern and less finicky) if it were available, and a hitlist of companies ripe for displacement (due to running old platforms) would help the vet as much as help the devs."
The benefit of change has to outweigh the cost. How long would they have to close, or "click over to the old system" with clients, until they were fully transitioned? These are not organizations that use webapps as their primary app delivery platform. (Or, rather, they don't know that's an embedded IE control in their x-ray viewing application.)
Who cares about the devs? Seriously, they are the group that should be paying for access to the markets, either via currency (buying software that makes this problem go away) or by labor (maintaining ten versions of their sites).
The problem is that most developers, and web developers especially, are squatting on the properties of large organizations with goals that are not always aligned with theirs. At best, we own our way down to the OS system call level. Increasingly, our dependencies are bound much higher in the application stack. .NET and Java versions can be changed out from under us, web browsers can be swapped out, and even features such as HTTP pipelining or keepalive can force us to reevaluate our scaling strategies.
I agree that the lack of control is frustrating. This is the nature of the industry.
For an example in another industry, read about Swatch Group's desire to stop supplying watch movements (and parts) on the open market. ETA has become so central in the industry (very similar to a late 90s MSFT) that the Swiss government became involved in slowing the policy change of a corporate entity. Even so, a number of smaller watchmakers will cease to exist because they won't be able to adapt.