It is possible that only needing one tank rather than two can make up for the dramatic loss of Isp we see from an air-breathing engine and the air-handling structure, but no one has yet managed to demonstrate that, and the general consensus runs against it. I recall reading that HOTOL (https://en.wikipedia.org/wiki/British_Aerospace_HOTOL) calculations were actually driven by an extremely light structure estimate rather than the airbreathing engine, to the point where if you plugged a rocket engine in they would actually get more payload to space as a SSTO, because those aggressively light structure estimates were doing all of the work.
Therefore nobody is ever going to invest the tens of billions required to develop a rocket based SSTO.
If somebody develops an engine that makes air breathing most of the way to orbit feasible, this has a chance of competing a Starship style architecture.
For the reasons you espoused, this is highly unlikely. However "highly unlikely" is more likely than "never".
Atmospheric density reduces exponentially with altitude, which implies that you would need to go exponentially faster to maintain mass flow into your engines and lift over your wings. The truth is that breathing air only gets you a third of the way to space, at best, so you have to have a rocket, and now you're battling that complexity. If your space plane doesn't breathe air, it probably is just better to punch your way out the way conventional rockets do.
Of course, the rocket equation is logarithmic, so reducing the amount of mass you loft gives you an exponential gain. This is true for all propulsion systems to an extent (different constants) but getting into space is the hardest propulsion problem we face. A space plane may or may not be better in this regard (it's been a while since I've looked into that kind of thing, so no opinion either way) but imo the inherent complexity is enough on its own to kill the idea.
The general idea is that you can get much better results in terms of deltav if you can find at least part of the reaction mass from elsewhere without carrying it onboard. Even inert nitrogen is useful as a reaction mass. Another way to get a good result is to use separate sources of reaction mass and energy. Then use that energy to accelerate the reaction mass as much as possible, so that you get a decent deltav by the time you exhaust the reaction mass. This is what ion and plasma thrusters do.
However, the requirement of the high thrust disappears once you finish the vertical climb. There's no danger of falling back to ground once you reach orbit. What you need at this stage instead, is to add velocity (deltav) to the craft to change its orbit/trajectory. This can be done even at very low thrust, because you have all the time you need. The limiting factor now is that you have only a finite amount of propellant onboard. You want to add as much deltav as possible before it runs out. A high thrust doesn't help because the engine will simply consume the propellant faster and exhaust it before you get the required deltav. This is where specific impulse comes into play. The maximum deltav you can get is proportional to the specific impulse of the engine (see rocket equation for details). As you can imagine, high specific impulse is critical for space missions requiring high deltav, like the New Horizons spacecraft that imaged Pluto or the Parker solar probe (interestingly, getting to the sun is harder than escaping the solar system). Rockets/jets with low thrust and high specific impulse are called sustainers.
The general trend seen is that specific impulse drops off as thrust increases. For example, the space shuttle solid booster has Tmax = 15 MN, Isp = 268s, and space shuttle orbiter cryogenic engine RS25 has Tmax = 2.28 MN, Isp = 452s. Meanwhile, the NEXT xenon ion thruster used in the DART mission has Tmax = 236 mN and Isp = 4200s. Note that the thrust has changed from Mega newtons to milli newtons. You would hardly recognize it if the ion engine thrusted against your body.