As far as I can see, URL shorteners – like goo.gl, bit.ly and many others – have perhaps three main purposes:
1. To avoid a complex URL being broken by being split across a number of lines by an email client.
2. To create an alias that is easier to remember (obviously not the random strings of characters) or to transmit by writing.
3. For the benefit of the sender, allowing tracking how much the links are used (not all shorteners do this but it is a key feature of, for example, goo.gl)
I think the first one was the root inspiration for the development of URL shorteners and would be ideally fixed by having email clients either handing long URLs more gracefully or automatically translating short versions back into a longer form before the user gets to visit them. Ideally those developing email clients would do both and then I think the market for shorteners would dwindle, meaning less steps for everyone in dealing with email communications.
It would also be good for web designers to think about making more use of what, for a time at least, were called beautiful URLs. For example, instead of this discussion being:
how about if we could access it as:
That would be short enough to type or even remember and is also richer with human readable information as a benefit.
The third reason is only a benefit to the sender and might even be seen as undesirable to the recipient. As someone who quite often uses shortened URLs to avoid breakage in emails (although I often include the original too) I do find it interesting to see how much the links are used but that is an opportunistic extra and not a good reason for such URLs to persist.