I thought the argument was that rockets spend a lot of fuel just getting through the thick low part of the atmosphere, which is the same point at which they're heaviest. Skip the start & you need less fuel.
That statement is misunderstood. Google "rocket ISP". Rocket engines work less efficiently at lower altitudes, and cannot be properly optimized due to the rapidly changing pressures between sea level and the near-vacuum at altitude. They burn extra fuel due to this inefficiency. And since rockets are at their heaviest in the lower atmosphere, even little inefficiencies really add up. Atmospheric drag is next to nothing in the equation. Even speed isn't the issue. It is about how they cannot design an efficient engine bell to cover the initial climb.
So if you can get above the thickest part of the atmosphere, say attached to a giant goofy-looking airplane, before you light off your engine - rather than having to push your way through that same thick air on your own - you need less propellant, overall, to reach orbit, which means you can devote a larger fraction of your launch vehicle's mass to payload.
Space shuttle was 3 g - 1 from gravity = 2g net acceleration, but that's kept low for passengers. Even then 2 g net ~= + 44 MPH every second.
So, first 15 seconds your going under 660 MPH which is not that fast, but you get ~1.4 miles up. Because drag increases with speed very quickly the next bit is harder, but you very quickly get above what an aircraft could take you with ~5.6 miles at 30 seconds. Note: Higher g's mean more drag in denser atmosphere, but less gravity drag it's a meaningful trade-off.
However, aircraft's velocity is very useful essentially saving those first 15 seconds of full burn, but comes at the price of needing more structural elements to support the hanging rocket.