That is right and in this case, "un large manteau" and "un manteau large" would be acceptable since the nuance between the two is very very thin.
In my view, "un large manteau" was designed to be loose in fit, while "un manteau large" is probably a couple of sizes too big for the person wearing it.
Beauty, Age, Goodness, Size is a shorthand method of classifying adjectives for positioning in a sentence.
Subjective/ figurative adjectives go in front of the noun they modify. Objective/ literal adjectives follow the noun they modify. Using the B.A.G.S. convention simplifies determining whether a particular adjective is regarded as subjective or objective given that adjectives are subjective by their nature.
As Sitesurf points out pants that are appear loose fitting by nature would be subjectively large whereas comparing extra, extra large size pants to your normal medium size would be placing large in an objective condition. I don't like these subjectively large pants because they are unflattering. I don't like those objectively large pants because they keep falling down when I wear them.
In ordinary French conversation no one will call you out and ask ...Do you mean you really, really believe those pants are large or are you certain that they are?...However there is a common practice with regard to adjective placement which you may be expected to express on an exam or resume etc.
Since Duo considers carry to be an unsuitable translation for porte in this context what would be an alternative French commonplace word to refer someone to actually carry a large coat.
I mean Duo's correction refers to do not confuse wear and carry as if there would be a more likely word for carry, and that wear is the most likely use one would expect for porte.
The weather must be a little nicer where you are.
I have all my jackets modified so I can carry a hat and/or gloves with me at all times. For about half the year I wear a backpack so I can carry outerwear in it. I always carry a snowmobile suit and bush boots in my car (it's part of what is called a blizzard bucket) in case I get immobilized in sudden extreme weather.
I spend more time thinking about what clothes I am going to carry and how I'm going to do it than I do thinking about what I'm going to actually wear.
But I take your point, most people don't have to spend much time worrying about the most convenient way to carry items of clothing.
F.W.I.W. three dictionaries place wear third or fourth in a list of definitions for porter. (Carry is first)
Goorgle translates graphs the usage as being equal between carry and wear. (presumably they are measuring the web) I don't have too much confidence in their translating ability but I imagine Google's web metrics are the best there is.