I should point out that I am English but I have lived in Poland 13 years. I am not anti Polish tradition. I am anti cruelty when it is not needed
The reason they sell live carp is that carp is one of the shittiest fish out there. When you buy it live you're expected to keep it alive for a couple of days, swimming in some water but not feeding it so it shits out all the mud and "stuff" before you kill it and prep it for food.
You might conceivably create carp resorts and vacation centers where carp would be starved in more humane ways, such as bigger pools, but starving is inhumane in itself too. So no matter how you slice it (no pun intended) eating formerly alive creatures is pretty cruel. If you decide not to starve carp before consumption then you'd be advocating what Varsovian suggested - cruelty towards humans. You don't people to eat mud, do you?