Yes it does, because you could tie your fiat payment ID to that robot lets say it was paypal your address and reciept can be used to deanonymise you so the more transactions you have one one bot erodes your privacy, theres nothing wrong with using the same bot you can go to town on it

I think for the average user switching bots makes no difference, but for a power user, you have to accept the trade off and the asking for a new bot everytime.

I do think its helpful if you're a trader using different payment methods so you could have bots set up for each pair you're trading which can make managing trades easier for some