At work, I'm not allowed to install arbitrary software as well - but policy doesn't make my workstation any less of a computer. Also, not all smartphone vendors are as anal as Apple, and there are always workarounds [1],[2].

I don't think we actually disagree - it's just a matter of definition; please note that I intentionally didn't say (personal) computer, but (general-purpose) computing device.

[1] http://en.wikipedia.org/wiki/Rooting_%28Android_OS%29

[2] http://en.wikipedia.org/wiki/IOS_jailbreaking

I would draw the line at what the device's technical capabilities are, not what I am "permitted" to do.

If you use permission in your definition then it becomes impossible, by definition, to restrict the use of a computer. If Dell's next cheap desktop was locked down like Apple locks their devices down, would you buy "Well it's not a computer you know, since you are not allowed to run what you want on it."? No, of course you wouldn't.

That's the norm with Apple, remember "You don't really need MMS and Cut/Copy/Paste do you?"?