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algebraic geometry is not my field at all, but it seems like this is a bit of an answer, and i don't really know the details but maybe someone can fill them in. TThre zariski topology is not good for doing homotopy theory. I have heard this at many seminars, specifically from someone who does motivic homotopy theory. So from that perspective it is not the right topology, but i can only say that i have heard this not that i understand why the zariski topology is bad. I guess just naively it seems like it would be pretty hard doing homotopy theory on "any" line where your only open sets are finite complements.