I see no reason why we couldn't have a DAR sticker and any member can propose it by following the directions for adding a sticker.
I am not sure I agree with the idea that there can be "too many" stickers. There is already a limit in place of how many stickers can be on a profile. Creating a new sticker doesn't change the sticker limit but rather gives the profile writer a broader selection of tools for writing and developing a biography.
There are already an infinite number of stickers based on some of the generic templates that can be custom tailored to fit any particular profile. The migrating and non-migrating ancestor stickers and the occupation sticker can be customed to tens (hundreds?) of thousands of different possibilites based on location, flag, occupation name, and occupation image.
An important component of genealogy are the many genealogy societies that aid amateur and professional genealogists and serve as a meeting and sharing place for genealogical knowledge. Both lineage based societies (like DAR and NSSAR) and those that have open membership like your local County Historical Society or the International Society of Genetic Genealogy serve an important place in genealogy.
Having a sticker that identifies a member or an ancestor is a valid and useful tool to help others identify profiles that may have clues to help break down brick walls. And stickers are used by members to show pride in their own genealogical activities and the contributions of their ancestos to history.
So by all means, create a post for a DAR sticker and I'll add a + comment, upvote it, and I'll even help you to get it added to the Society template page.