I agree with OP that (if technically and financially feasable) characters from
[anchor text] shouldn't be counted when using
[anchor text](URL), in regard to the 600-chars limit. But I can imagine money and resources might be an issue.
I have the (maybe ungrounded) fear that they will expire at some time. Further more, if a given URL changes over time, the heuristic work to find back data (e.g. using data from Wayback Machine would possibly be made more difficult. I can imagine other automatic or manual retrieval/linking/archival issues can arise (e.g. automatic: regarding recursive link retrieval depth)?
Wikipedia offers several examples of URL shortenings' shortcomigs, such as linkrot and an additional layer of complexity (additional HTTP requests and DNS lookups) increasing latency. A change in service of the shortURL's provider such as intervenient ads, may also give unwanted behavior.
Big data issue?
@Aaron Bertrand - I know too little of big data to understand the point (I guess, you might correctly make) about the cost and troubles coupled with expanding of the database columns.
Nothing changes in end-user's design
On the other hand, I think, from the viewpoint of the non-changing final readability and compactness of design and thus (at least in that sense) the unjust punishment of the end-user (who just happens to link to a long URL), ought to be avoided.
Decaying of the comments
The decaying of the comments can be relevant to this question, as URL-shorteners are (in the answers above) thought of as the best way to circumvent the problem at stake; that is when the comments would stay transient → then the URL-shortening services are thought not to change too dramatically or expire before the comments (however, I can imagine URL shorteners can certain technical difficulties for crawlers and the like; see URL shorteners in this answer).
I wasn't aware of their decaying (cf.
Comments are temporary "Post-It" notes left on a question or answer.). My first reaction is that this ought to be perceived as an intellectual loss (although I can agree, this is currently perhaps a technical facility in some regards); certainly when perhaps in the future, data storage and serving would become much more efficient and cheaper. Comments, even erratic ones, provide valuable context and enriching discussion. Some voices say an option to make them permanent should be added. If for some design reason; one would like to hide comments; this can still be done, whilst saving those comments.