Okay, here's the math.
Suppose an east-west front oriented along the 'x' axis and passing through the center of your (two-dimensional, carthesian) world. Your journey starts 200 miles south of the front (which is 0, -200) and ends 200 miles north (0, 200). There is a 20-knot x-wind to the left for the first bit, and 20-knot x-wind to the right for the second bit. Airspeed is 100 knots.
If you do not compensate for the x-wind but simply fly a magnetic heading of due north, you end up two hours later crossing the front at the (-40,0) position, and yet another two hours later at your destination (0, 200). The crosswinds have cancelled each other out, and the distance traveled through the air is 400 miles. So a four-hour journey. (Ground speed, by the way, is 102 knots so the distance traveled over the ground is 408 miles.)
If you do compensate for the x-wind you've got to compensate by approximately 12 degrees to the right on the first bit, and approximately 12 degrees to the left on the second bit. (Approximately 12 degrees is calculated by the 1:60 method. In reality sin(angle) = 20/100, or angle = 11.53 degrees.)
So true heading is 012 degrees, while true track is 000 degrees. Ground speed is 100 * cos(12) = 97.81 knots.
So you cross the front at (0,0) after 200/97.81 = 2.0447 hours (2 hours and 2.6 minutes). After the front the same calculation applies, but you fly a heading of 348 degrees. And another two hours and 2.6 minutes later you reach your destination (0,200). Total flight time four hours and 5.1 minutes.
So in this idealized situation not compensating for the crosswind is more efficient, though only marginally so. In practice, like I said before, considerations like airspace, navaids, predictable flight paths for ATC and so forth will be more important than shaving the last five minutes of flight time off a four hour journey.
On the other hand, the stronger the crosswind in relation to TAS, the greater the difference. In the ultimate case, suppose the crosswind is equal to your TAS. If you compensate for the crosswind you need to put your nose directly into the wind, and will not get anywhere. You will simply "hover" above your departure airfield until the fuel runs out. Whereas if you just point your nose to true north, you cross the front at the (-200,0) position (crosswind drift to the west being equal to the distance traveled north), and you drift over your destination (0,200) again exactly two hours later. (How you take-off and land in those conditions is an interesting one, but not relevant to the problem.)