I'm arguing principles, BJL. The badges should be separate if they want to make the sponsorship (paid advertising) a truly optional element of the shirt. Or, it should be on the shirt, with the sponsorship used to lower the cost of the normal shirt. In that case, I gladly take the sleeve sponsor for a lower priced shirt; unfortunately, that's not the way of the world (especially these days, where entire advertising teams exist to find ways to further squeeze more money of out consumers for fabricated "features": "Now you can buy The special edition "Speedo" Porsche, which is twice as fast on the track as the standard model, as we've removed all the nice bits that added weight").
To your second point, of course it is, but my argument has nothing to do with from where the main benefit to the sponsor comes—why would it be when we are discussing supporters paying to add advertising to the shirt for a company paying the club to advertise it's brand. That is a separate factor entirely and I agree with your thoughts.
All that said, maybe this discussion is more suited for Off Topic, so I'll let it go.