> Written for longevity
OSS is much better at longevity than proprietary. Even if the authors all die without will, it is possible to fix the little bugs that prevent you from using the software on [NewTechnologyHere]. I've done it countless times with Java software; If anything OSS is the guarantee that you own your future and that the system will exist in the legacy.
> Use paid flavor
It's good, but what's better is joining the golf club of a principal maintainer. He's key in paying him to fix the issue you're having quickly and merging upstream.
Long, long ago when I worked at Nortel (a now defunct, but then huge telecommunications company), they used to pay millions of dollars a year to Cygnus to support a particular embedded version of GCC. This, despite the fact that Nortel had more than 10k programmers on staff including a compiler team!
I think the real reason these support contracts exist is because companies (even large ones) don't want to dilute their focus maintaining projects that are peripheral to their core business. It's not so much a technical problem, or a money problem -- it's a management problem. They can't scale out to handle every little thing.
I think OSS is a red herring in this conversation. Most companies just don't care about that. They don't want to support it themselves (even if they are big enough to do so), and they need to have confidence in the company that provides the support. Build that company (hint: you need to be sales heavy!) and you could sell Postgresql just as easily as any other database. Of course breaking into an entrenched area in Enterprise software is always going to be difficult, so I'm not sure how successful you would be with this particular product, but you get my point, I think.
As hindsightbias puts it they want solutions and 24*7 support.
Many also think looking up issues on stackoverflow, google or blogs as unreliable. Then there are times when issues might be specific to installs or data, in which case sharing the logs/sample data (even masked ones) can be risky. They feel comfortable sharing logs/masked data with for example Oracle because they believe it to be safe and locked under Oracle's security guidelines.
The 2nd refrain I hear is - security. In case of a major security issue being revealed, there is a general sense that FOSS will be slower to react in releasing a "stable" patch. Comparatively paid software take it as a reputation risk and work towards quickly releasing a "stable" patch.
If people have to use FOSS, then they try and search for the paid support flavor. Recently we were looking at MQ software. When we zeroed in on RabbitMQ we were asked to deploy only the paid Pivotal version and not the free version because "support".
Sure, these things might not be completely true but for many higher ups paying for something somehow makes them sleep better at night than a "free" alternative.