For 7 years I had the same vision about frameworks and swore I would never use one:
a) Because, like you, I felt like it was cheating a bit and
b) I couldn't see how they would benefit me
But....
I recently started work for a new company who use the CodeIgniter framework and I now take it all back!!
I think it's important that you still know how stuff works with pure PHP such as file uploads, sending of emails, using sessions and cookies etc etc but for large applications, frameworks definitely are a benefit.
I don't think I'd use one for a small site/application but for larger ones in the long run it saves time and forces you to code consistently. It also takes care of things like error handling and comes with loads of built in libraries (eg. Shopping carts).
I haven't tried Zend, CakePHP or any other frameworks but I must say, I think CodeIgniter as a first framework definitely teaches you the basics of working with frameworks as I believe it's the simplest.
Like I say though, I still think it's important you understand how stuff works regardless of frameworks if you're looking at coding in PHP for years to come.
Hope that helps somewhat.