People seem focused on the interpersonal conflict angle in the comments here, i.e. winning and losing in a battle of wills.
I think its just as important to realize ideas themselves can be conflicted or contradictory, and that practical action requires compromise. Many seductive ideas may not be well-formed if you really dig deeply enough. It's not just economic or political pragmatism. Even the solo designer/thinker needs to compromise such untested ideas in search of a realizable system.
I believe people are focusing on that because that's a traditional meaning of the word — Merriam-Webster uses "concession" in 2 out of 3 definitions. I would say that an impersonal "compromise" was more of a figure of speech that evolved into another meaning of the word.
The OP here talks about a compromise between two ideas, which means that it could be a single person making trade-offs based on their conscious choices about where the (bigger) value is.
The negative connotation is also mostly personal — it's like glass half-full or half-empty question: one can say that in a compromise, two people/ideas are going away with some of their desire/value unfulfilled, or that both are going away with some of their desire/value fulfilled.
Well yes, as a designer the thing people do not understand is that e.g. for a poster there is a limited bandwidth for messages you can get across. The "uncompromising" business guy may think he is uncompromising by putting all infos he really wants to push onto the poster, but in fact that just means they are deluding every single message they really wanted to push.
In reality you always have to compromise if you aim to achieve more than one thing at once. Wanna deliver a quality product and earn money? Then you will have to compromise between the quality and the revenue in some ways. Granted if you search hard you may be able to find ways (=compromises) that are more win-win on both fronts than others, this search is the task of any good designer.
But that means you have to have at least have to have a slither of understanding of the search space.