That's not the reason you don't use it for a first stage. The disadvantages of hydrolox (which are numerous) are offset by its incredible specific impulse. But for a first stage, specific impulse doesn't matter that much, while thrust matters a lot. Thrust is in large part proportional to fuel density, as a turbopump sweeps out a fixed volume per rotation, so the denser the fuel, the more mass (and generally all else being equal, energy) it pumps per rotation.
Another aspect is that first stages are big, meaning that cost is more important than specific impulse. By contrast, when dealing with an upper stage, a small increase in mass has a huge increase in first stage size, and since first stages are so large and expensive, that's a big cost. So you generally want a higher ISP upper stage. With the caveat that "storability" requirements for engines that need to restart can shift the balance; because hydrogen is so deeply cryogenic it's difficult to store for protracted lengths of time. Also, the longer you plan to have a stage in usage without maintenance, the more you tend to favour simple propellants over high performing ones, particularly when you're dealing with small, light engines. So for example if you have an interplanetary probe you'll tend to favour a self-pressurizing hypergolic system so that you only have to rely on a couple valves working, even though self-pressurizing propellant tanks are heavier and hypergolics tend to be lower specific impulse. Engines that are smaller still are often monoprops for an even greater degree of simplicity.