With rockets, faster acceleration means LESS total fuel to orbit, not more (assuming you can just use the same fuel either faster or more slowly). The shorter time you are fighting the 1G, the less total fuel you use up. Imagine takeoff to orbit at 1.01G (1G earth, .01G motion). instead of 2G. You take forever to achieve orbit and the first 1G is wasted all that time.
The only advantage I see is (as you say) lighter engines and structure. Still seems low compared to any other rocket I have ever seen.