While it may not be directly important to the final users (if you don't count security upgrades between versions), it definitely impact the ecosystem. If you need to pick a platform to develop for, you go for the more homogeneous one from a OS point of view. Also enterprises invest more in devices that have a longer support life. They want to buy something that even in 2-3 years is fully supported by the manufacture.
Enterprises don't care about device support life. They care, if the phone will survive for about two years. Then the employees will start bug you, that they want new gadget (I know, we have several hundred of them...).
Hard to say objectively, but I believe that actively updated software enhances perceived value. The human mind, even the non-technical one, is deeply attentive to change - as website iterations show, subtle improvements can have huge payoffs and even feed into the mind's reward circuitry. Every time there's a round of iPhone updates, I run into more than a few "normal" people that are delighted by tiny new features (anything from background wallpaper to iMessage read receipts). To people that don't usually keep their software up to date (but are coaxed into it by iTunes and now iCloud), getting new abilities without cost or effort is especially cool/rewarding.
Do you have any specific APIs or features in mind?
I think most app devs look at the installed base numbers and choose to support 2.1+ or 2.2+. I can't think of any APIs in 2.3 or 3.0 (or even 4.0) that are so wonderful that they are worth cutting off such a large part of the potential customer base.
So in that case, what about customers who DO buy new devices? Your argument suggests that developers won't build software to target the new capabilities their devices have. In which case the manufacturers' refusal to keep their old devices up to date is actually undermining their ability to sell new hardware ("Why should I buy a new android phone; all the software is written to target my existing two year old model")
There are many ways to make a new device attractive besides making it incompatible with old devices. Support for new radio standards. Larger, brighter, higher resolution screens. More flash storage, a better camera, more attractive industrial design, more built-in apps, and a more polished UI for built-in apps.
Will this sort of backwards-compatible improvement always be possible? Probably not. Someday all the specs will be maxed out. But for now it's a good strategy.
OS updates are probably more important for developers initially---having access to the latest and greatest API/phone features/bugfixes. This becomes important for consumers when the apps they want to use require a version of the OS they can't get.
I agree they're maybe not essential to a lot of consumers. Lord knows most people never thought about whether their dumbphone's OS was outdated or not, but I do think it's less than ideal for the ecosystem in the long term.
In terms of perceived value? Definitely. See all the flack Apple received for not supporting Siri on the iPhone 4. Now imagine if they hadn't released iOS 4 and multitasking on the 3GS.