Hmm. The purpose of the {{LinkArr}}, {{LinkEd}} and {{LinkTr}} is to create sub-sections on the main category page for the person concerned, where these are listed together with any compositions of their own. Would we want {{LinkDed}} to work in the same way, with a heading for "Works dedicated to xxx"?
To be honest I have serious reservations about this, since the category page has the clear purpose of listing works to which the person has contributed, and that would become a little fuzzy if lots of other works were listed, some of which could date from centuries after the person's death. And wouldn't it be tempting for aspiring new composers to upload their brand new compositions with copious dedications to Beethoven, J S Bach, Mozart, Schubert, etc., so they would be prominently listed on the category pages for these famous old masters?
If the dedicatee already has their own category. I currently use the "{{LinkName}}" template for dedications, Since many dedicatees are friends and family members of the composers, and often not even musicians, they wouldn't ordinarily qualify for category pages on IMSLP in their own right. And as Emery has pointed out, identifying the person meant by "To my dear Sasha", etc., wouldn't always be easy, not to mention the works dedicated to institutions or places that would be difficult to handle.
If we make sure that names of dedicatees are written in full (maybe in addition whatever affectionate tributes are written on the score) then these should at least come up using the search button, and the "What Links Here" facility will find anyone referenced by {{LinkName}} who already has their own person category. There are a huge number of librettists, arrangers, translators and editors whose names have still to be linked, so there's still plenty to be getting on with...