What a weird analogy. Putting a logo on any product is called branding. So a logo on a prosthesis is just having a branding on oneself. Which is a much more powerful analogy, even at the cost of being a tasteless pun.
It's actually a perfect analogy, IMO. Tattoo, is a form of (typically chosen) self-branding. A lot of companies make great products and then deminish them by thier mis/use of branding. Usually in a tactless way. This is a prime example of that.
A lot of people buy products because of the branding. How many people would buy a YETI cooler if or a Coach bag if it didn't have the branding to show off that they have a YETI cooler or a Coach bag? It's conspicuous consumption.
I think those two in particular might be poor examples, since they generally do quite a bit of de-branding on their products. I know what you mean however. Supreme is a prime brand for this. Nobody is buying a Supreme t-shirt for any other reason than the logo. Whatever thoughts on people who buy things to impress others may be, those kind of people exist and to each thier own. They at least made the choice to let everyone else know what they value.
I see where you're coming from, but a prosthetic arm is someone's arm. Mentally it very quickly can become something you identify with, like a prosthetic arm basically being YOUR arm.
When you then have your prosthetic then being an advertisement, it can have an impact on your relationship with the device.
I don't want someone branding my arm and I can see why others would feel the same.
You're right -- I totally misread what you said. Sorry!
I think tattoo does imply more of a permanence and familiarity in regards to the relationship someone would have with a tattoo on a part of their body they're born with, but I do see your point as well.