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Off course it cost energy to drive a balance shaft, but I don't think it's much more than marginal in the end, if the bearings are ok. A balance shaft is in trouble from birth, simply because it's purpose is to cause imbalance to counter act the imbalance made by the pistons and rods. The piston-, rods-, and crankshaft assembly is on the other hand designed to be as smooth as possible, but doesn't make it all the way, hence the balance shaft in some engines. I don't find it strange that the balance shaft bearings may wear out quicker than the others.
The old German Ford V4 ("Cologne engine", used in Taunus and Saab 95/96 of the 1960's and 70's) is very prone to wear out in the balance shaft bearings. You can sometimes get an early warning if having an oil pressure gauge. When the bearings fail, it's not uncommon that the fiber plastic gear goes with them, and that will stop the water pump, the radiator fan and the alternator. That happened to me once, and after the failure the engine was running rough, but more silent, without the whining noise from the alternator. A 60 degree V4 without balance shaft is however way worse in balance than a straight-4.
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