so far, I read a lot of differentiated semantic qualifications about 'what is a product.'
Those who teach, consult, are selling a service. They bring what they know, impart the knowledge, tutor a student or client in developing skills in the particular area needed, and though concentrated thought and real effort go into it (the work part) the teacher or consultant does not walk away from that job with less of that product needing to be resupplied. That is very different from manufacturing gross upon gross of ceramic mugs to supply diners and restaurants, or stores, throughout a large area.
A singular work of art is also 'product,' but it is a one-off. Recreations of that work (concerts, plays, ballets, recordings, etc.) remain 'product' while the original work, currently under copyright, is not essentially 'sold off' like the ceramic mugs.
An artist takes a commission for a work from an individual, musician, group of musicians or a symphonic organization, and it is understood that 'the product' will be delivered as per contract stipulations. This is more clearly 'product,' and 'consumer,' or customer. Commissions are by nature specific, as to at least the instrumentation and duration of the work to be produced. Often, in the fine arts arena, those are the only stipulations, with perhaps a request from one player or ensemble that the work's content will show off a player's particular strengths, or an ensembles' particularly strong brass section, for example. In this area, artists are well aware of 'creating a product to order,' and many do just that. Still, this is all a very far cry from the more commercial aspects of marketing, study upon study before any money is spent on a prototype which is then tested on a selected group of potential buyers.
I do think it healthy for artists to realize what they make is, if to be sold, a product of sorts... as some do not realize even that much, though it is usually the youngest amateur or student who does not 'quite get that... yet.' When I schooled, there were constant reminders from my comp teacher about the pragmatica of the business, i.e. writing first for smaller ensembles where you had a chance of directly finding your own performers; not using that mandolin for just one bar of an entire piece because that would call for a separate union player not a usual part of the orchestra and rack up another full union wage; that the moment the score called for the multi-instrumentalist (third flute going to alto flute) the player in rehearsals and in performance, as per union regs, would be payed time and a half; that if you are established like Stravinsky you could ask for and expect to get a contrabass Sarrusophone in that large orchestral work and the additional cost would readily be met -- if you were not yet established, not to even think about it, etc.
Many pros in the arts routinely work within these types of restrictions, commissions now often coming from two orchestras, which can 'flatten out' what instruments are available, i.e. what is common to both, and there is no telling from the work there were any limitations whatsoever. This is radically unlike the more commercial end of commissioned music like scores for film and video games, where the director has a full say in the type, style, mood, etc. and the composer must comply. Relatively, the classical composer who is commissioned still has parsecs of latitude in what they write and how it sounds.
I don't know why that distinction is so difficult to make, or why a proposal of how to market a singular work of art should be pounced upon as if it could / should be marketed following the model of selling the ceramic mugs. Both the mugs and art are sold, the model from one mode of marketing just about as foreign to the other as could be. Multiple copies of artworks, recordings, repeated concerts are in another realm yet again.
When it comes to music, multiple copies of the score might be sold or rented (like buying those more generic blueprints to make a house, someone other than the composer / architect still must provide the necessary tools and labor to realize it), but the rights to the piece or architectural plan itself are not 'sold.' It is not anything like the ceramic mug, i.e. when the demand for another piece or another blueprint comes in, you don't just run off another exactly like the last one... and there I get some sense those coming from the more consumer-product angle of marketing seem to ignore that completely.
It is not stunning news that what a teacher or consultant or artist provides is not a mass-manufactured ceramic mug, but I find it rather stunning some would reduce all of those and plunk them under the same category of "product" and then apply the same principles of marketing for the mug to the more singular types of services or works of art.