Holes in tubes create stress concentrators. The sharp edges around the holes can start to fail and the crack propagates into the nearby metal. If this happens while you are riding, you could be seriously hurt or killed.

If you get drillium fever and drill through stuff on your bike (like chainrings, brake levers, etc) make sure that you chamfer every hole to reduce the stress concentrator effect. Also, you can put a ball bearing on the hole and whap it with a hammer. Properly done, this cold-forges a chamfer into the hole edge and should reduce failure rates.

To optimize tube weight, we engineers came up with drilling a big hole down the center of a rod, yielding a tube. Actually, tubes are usually drawn over a mandrel. To do the weight-lowering process one step further, we use a process called swaging, to thin the tube wall in the center of the tube. This yields butted tubing.

If you want a hippy-dippy bike that makes the sound of a pan-pipe as you ride and may break at any minute, go ahead and drill through the tube sideways. If you want a light bike that is safe, trust the designers, engineers, and artisans that produce butted tubing. They've already "drilled" the tube - axially, down the center.