I understand your concerns, really do. And I can totally understand why you want to stay away from that model, more power to you. Choice is a good thing. But I think any of these doomsday cases are highly unlikely.
Any properly designed elastic computing structure can be restored through all manner of disaster scenarios - so the scenario of a server farm and all it's data permanently and irrecoverably going up in flames isn't plausible. Modern server infrastructure simply eliminates those scenarios. You can have service interruptions, sure, but complete loss of data. Nope.
The scenario of Valve going under, or being bought out, or whatever manner of corporate evil you might want to imagine is certainly more plausible. And you're right about what the EULA states. But EULA's are not absolute, they exist in a legal gray area, expect the law to develop over time as challenges are made and the world transitions to digital. If Steam were to go under and leave some 125 million users up a creek without a paddle, you can bet there will be litigation from some of those, regardless of whatever the EULA claims. In a case that would affect so many with clearly identifiable damages I could easily see action to release server code to reverse engineer the service dependency, i.e. "jailbreak" the software. It might be a mess and take some time, but it certainly could happen.