Analysing what those things are seems a good idea if you're trying to emulate it, and you can't do that by "Trying the app yourself". The best way, as the OP has done, is ask customers why they pay for it.
I have tried Campfire, and I'm still not quite sure why people pay for it. I think you can take simplicity too far personally. It could be replicated on a weekend (As was done at google with huddlechat) so I don't see the value proposition there. I haven't tried basecamp so maybe that's more complex.
For example, compare Highrise with Salesforce. My company (a 50 person consulting firm) is moving away from SF to HR right now, even though SF has many, many more features. Why? Because HR has all of the features we need, and most of the features we like (but don't absolutely require). And we are much, much more productive when using HR. It's easier to use. I don't have to think much when filling in information. The reports take me about 5 seconds to read and comprehend. This time savings is very valuable to me and my company - I've got better things to do than think about how to use a CRM application. The features Salesforce possesses that HR lacks, by contrast, don't have any value.
You'll get it if you just look at things through a slightly different lens. You might be getting tripped up by the confusion of effort and size with value. Value is what software has to a customer - effort is the cost software has to developers. And size is just a number. It would be nice if these three number always correlated. But unfortunately, that isn't the case.
The iPhone looks extremely simple. But it's a ruse - it's actually massively complex and a feat of engineering. It's hard to copy.
I agree, it takes a lot of thought to decide what to leave out - lack of features can be a good thing. But those decisions are not really defendable in terms of IP (Unless you complain Huddlechat 'stole' your whole UI and they roll over)
I haven't used basecamp or highrise extensively, so perhaps they make up for campfire.