The machine terminal vendor makes some and the merchant gets the rest of what's skimmed off.
To be honest, I don't know the terms of the transaction, but in my experience, most merchants are as annoyed as I at the offer, and would tell me to pick euros without prompting, sometimes even selecting euros for me. Publicly, by the banks, it is presented as a "convenience" for the traveler, so there probably are some merchants who believe the hype. But overall, I do not get the sense that a merchant has pressured me or gets any cut off it.
The terminal flips to DCC when it recognizes a foreign credit card
True, your credit card has quite a bit of information about you in that strip or chip.
You don't get DCC if you tap, which has a fifty€ limit
Not in my experience, or at least in Spain, tapping would bring up a DCC option on occasion, and I was able to use "tap" for purchases over 50 euro, the only difference is I would sometimes be prompted to punch in my PIN (My travel credit card is true chip and pin, with pin priority) It varies by country, the credit card processor, your card requirements, and even the type of merchant.