The point wasn't that the discussion is stupid, but that believing particles can be in two states at once is stupid. Schrodinger was doing a kind of argument known as a reduction to absurdity in his paper The Present Situation in Quantum Mechanics. He was saying that if you believe a single particle can be in two states at once, it could trivially cause a chain reaction that would put a macroscopic object in two states at once, and that it's absurd to think a cat can be in two states at once, ergo a particle cannot be in two states at once.

In his later work Science and Humanism, Schrodinger argues that all the confusion around quantum mechanics originates from assuming that if that particles are autonomous objects with their own individual existence. If this were to be the case, then the particle must have properties localizable to itself, such as its position. And if the particle's position is localized to itself and merely a function of itself, then it would have a position at all times. That means if the particle is detected by a detector at t=0 and a detector at t=1 and no detection is made at t=0.5, the particle should have some position value at t=0.5.

If the particle has properties like position at all times, then the changes in its position must always be continuous as there would be no gaps between t=0 and t=1 where it lacks a position but would have a position at t=0.1, t=0.2, etc. Schrodinger referred to this as the "history" of the particle, saying that whenever a particle shows up on a detector, we always assume it must have come from somewhere, that it used to be somewhere else before arriving at the detector.

However, Schrodinger viewed this as mistake that isn't actually backed by the empirical evidence. We can only make observations at discrete moments in time, and to assume the particle is doing something in between those observation is by definition to make assumptions about something we cannot, by definition, observe, and so it can never actually be empirically verified.

Indeed, Schrodinger's concern was more that it could not be verified, but that all the confusion around quantum theory comes precisely from what he called trying to "fill in the gaps" of the particle's history. When you do so, you run into logical contradictions without introducing absurdities, like nonlocal action, retrocausality, or these days it's even popular to talk about multiverses. Schrodinger also pointed out how the measurement problem, too, directly stems from trying to fill in the gaps of the particle's history.

Schrodinger thought it made more sense to just abandon the notion that particles are really autonomous objects with their own individual existence. They only exist at the moment they are interacting with something, and the physical world evolves through a sequence of discrete events and not through continuous transitions of autonomous entities.

He actually used to hate this idea and criticized Heisenberg for it as it was basically Heisenberg's view as well, saying "I cannot believe that the electron hops about like a flea." However, in the same book he mentions that he changed his mind precisely because of the measurement problem. He says that he introduced the Schrodinger equation as a way to "fill in the gaps" between these "hops," but that it actually fails to achieve this because it just shifts the gap between from between "hops" to between measurements as the system would evolve continuously up until measurement then have a sudden transition to a discrete value.

Schrodinger didn't think it made sense that measurement should be special or play any sort of role in the theory over any other kind of physical interaction. By not trying to fill in the gaps at all, then no physical interaction is treated as special and all are put on an equal playing field, and so you don't have a problem of measurement.

What a lot of people aren't taught is that when quantum mechanics was originally formulated, it had no Schrodinger wave equation and it had no wave function, yet it was perfectly capable of making all the same predictions that modern quantum mechanics could make. The original formulation of quantum mechanics by Heisenberg is known as matrix mechanics and it does not have the wave function, it instead really does treat it as if particles just hop from one physical interaction to the next. Heisenberg believed this process was fundamentally random and so at best you could ever hope to make a probabilistic prediction, so he treated the state vector as something epistemic, i.e. the particle doesn't literally spread out like a wave, it just hops from one interaction to the next and you make your best guess using probability rules.

Again, matrix mechanics can make all the same predictions as standard quantum mechanics, and so the wave function formulation is really just a quirk of a very specific way to mathematically formulate the theory, so assigning it such strong ontological validity is rather dubious as it is not indispensable. Superposition is just a mathematical notation representing the likelihoods of different results when a future interaction occurs, such as with your measuring device. It doesn't represent the ontological status of the system in that very moment, because the system does not even have its own ontological status. As Schrodinger put it, particles on their own have no "individuality." Physical systems only have ontological reality when they are participating in a physical interaction.