If you're accurate enough not to pee on the counter then the only thing holding back someone so inclined is the social taboo. It's not like the kitchen sink where stuff regularly goes in there. Does pee harm pipes? Will it make the sink bowl radiate a permanent smell? I just hate wasting water by flushing only pee but also don't like letting pee sit for an excessively long time.
You would still need to run the sink to clean out the pee. The minerals in your urine calcify if they're left to sit and they will sit in the pipes unless you run the water.
That uses way less water than flushing a toilet though