Basically, people don't like to be tracked, and we have no right to track them. Using URL shorteners would allow you to get loads of user details (depending on the service you are using, they can even be personally identifying information), so privacy issues would be a problem. Data that can be obtained can be, and not limited to:
The only shortener that is "allowed", is the default SE one. Which is a shortener for internal questions or answers. Example:
http://meta.askubuntu.com/q/11624/8698 which can be shortened even more by removing the last number which is your user id. Thus it becomes like so:
http://meta.askubuntu.com/q/11624. (this is the shortened URL of this question)
This shortener can get you no details whatsoever (Not as a normal user at least. Though moderators can probably see more data). The only details you get from that is when you get one of the following badges: Publicist, Booster and Announcer. So other than knowing that at least 25, 300 or 1000 user clicked on your link, you can't see any data.
For external URLs, you can try to remove most of its metadata (read the next part of the answer for more info) and make it much shorter. And the 600 characters limit is, most of the times, enough. In the cases where it isn't, I guess it's OK to add another comment. Or that comment can be an answer.
As for your idea of having the links not counted in the characters count, I'm not sure that would be possible as this can be a limitation from the database.
Most of the links in existence can be shortened just by removing some "metadata" from them. A lot can have extra stuff in them that are only used for statistics or SEO.
I'll take this question URL as an example:
The canonical URL of this question is
http://meta.askubuntu.com/questions/11624/can-i-use-url-shortenin-in-comments. Other than the SE shortener, you can take that link and strip out everything after the number so it would become:
http://meta.askubuntu.com/questions/11624. This last link would still open this question because the data that was removed is just used for better SEO.
Another example is Google Search.
Sometimes when you are sharing a Google search URL, you get lots of stuff in the URL. For example, in Firefox, when you are searching Google using the search box, you get a link like the following:
https://www.google.com/search?client=ubuntu&channel=fs&q=URL&ie=utf-8&oe=utf-8z. Most of the data that are being sent are just to tell Google that I reached Google using Firefox on an Ubuntu OS. Removing all that data, you will get:
https://www.google.com/search?q=URL which is shorter by 43 characters. Also, in most cases, you can even remove the
www. part from a URL to get even 4 more letters as in