〜がする is used to describe a sound, smell, taste, or certain other sensations that you perceive as coming from a particular thing or place. It is essentially about what you perceive at a particular moment rather than a permanent quality of whatever evokes that sensation in you. In that sense, it is similar in function to 〜が見える and 〜が聞こえる.
Sentences like ビールは味が苦い and 納豆は匂いが臭い are redundant and unnatural, where the subject is an abstract noun that refers to a sense and the predicate is an adjective that describes what sensation you perceive through that sense. This construction is closer to 象の鼻は長さが長い than 象は鼻が長い in that the subject is an abstract concept rather than a concrete thing like 鼻. This is simply not how you say it. You say ビールは苦い, 納豆は臭い, etc. just as you do 象の鼻は長い.
While not exactly redundant, バラは香りが甘い sounds unnatural for a similar reason. The difference is only that you cannot rephrase it to バラは甘い because the adjective 甘い is not understood as referring to a smell by itself as 臭い and a few less commonly used adjectives like 芳しい would be. You need a word to make it explicit that you are talking about a smell, and バラは甘い香りがする is how you say it.
バラは香りがいい sounds natural enough, though. It is understood as focusing on one specific aspect of the topic (バラ) and evaluating it in that aspect in simple terms of whether it is good or bad, rather than describing in an open-ended manner what its smell is like as is the case with 甘い. You can also use adjectives that describe intensity, such as 強い, in the predicate position like that.
バラは香りが甘い may sound natural as a response to the question “What is sweet about roses?,” where the questioner already expects roses to be evaluated in sweetness perhaps in comparison with something that is sweet in some other sense, most probably taste. Such contexts are not very common.
Though it is hard to answer why, it could be that we don’t see a smell in a whole-part relationship with respect to the thing that emits it so much as we do see a body part as, obviously, part of the owner of the body. I guess a smell is still seen as an ephemeral phenomenon that you perceive at each instance even when you think you are talking about a permanent trait of something, and this makes バラは甘い香りがする most natural. When the sentence sounds natural with an adjective in the predicate position, the subject (香り) is in a way forced to be seen as a part of the topic (バラ), or more precisely as one of various aspects of it. In other words, the sentence is still more about バラ, as seen from a particular aspect, and less about 香り itself. This expected focus on the topic seems to be distracted if the subject cannot be seen as a part of it in the
〜は〜が [Adj] construction.
バラは甘い香りをしている sounds odd to me, at least if you are talking about roses in general. It may be acceptable if you are talking about specific roses with a particularly sweet smell. I would expect the topic to be more specific in that case, like このバラ.
象は長い鼻をしている sounds equally odd to me. 〜をしている is used to describe a natural characteristic of a particular thing or person as you observe it. For example, you might say something like この象は可愛い目をしている about a particular elephant. When you do so, you are stating your observation. The nose being long is an objective fact about the species, and that is more naturally expressed as 象は鼻が長い.