tl;dr. : If we want the result of a quantum computation to have scalable more bits, we will need inner measurements to have scalable precision, if we already know the result of the computation (from a classical computer) then we could predict measurements with scalable precision! over the very physical system that constitutes the quantum computer, that seems to contradict uncertainty, and one of the two seem impossible.
What does it means for a Quantum Computer to be scalable?
Let's suppose scalable QC means just to compute bigger numbers, scalable precision.
A QC should be able to give deterministic and correct result over classical computations (deterministic here means known classical algorithm, verifiable results with classical computers).
While the quantum computation is done through measurements, its result need to match deterministic classical results, so it would be equivalent to say that QC would need to predict that very specific "quantum measurements" with an 'scalable precision' (predict measurements used by that specific computation). And that's the issue.
If we name a measuring device as "a measurement device" then physics say we can't predict the interaction with the measured system, but if we name it a "quantum computer" the interaction then seems to become predictable (and even with scalable precision!?)
In physics: a quantum physical system gives unpredictable outcomes (only predictable probabilities)
Quantum System => measuring device (not intended to do computations) => Measurement
In Quantum Computers : system gives scalable predictable outcomes.
Quantum System => measuring device (designed to compute + algorithm) => Measurement
Scaling vs Uncertainty
If scaling precision is to scale prediction, quantum uncertainty and quantum computing seems opposites, scaling in QC will be related with a reducing uncertainty in the measurement.
In the extreme case, if we can't eliminate uncertainty in the measurement, then QC would not be scalable (i.e there will be some problems or precisions where a QC won't scale, because if were scalable, it would let us to predict the outcomes of a measurement of any physical system or a specific system with scalable precision )
A classical computing analogy
In classical computers there is a threshold in its inner transistors, comparators, etc.. (to separate 1 from 0 and avoid quantum effects, noise, and so on), we use the probabilities of systems that we already know and carefully design, to mechanically compose an abstraction layer over them. Then to "scale" a classical computer, we have two ways:
1) just waiting the computer to spit more numbers.
2) making it bigger, scaling the amount of transistors, or faster, higher clock, lower threshold,etc..
But we don't scale precision by changing threshold in runtime, "by software", and QC would seem to do something like that, because as computation is done by the measurement itself, and not by any classical abstraction so prediction would depends of the precision we ask by software, as if we could change microprocessor to use 3.3v, 1.8v, or 0.00001v in Runtime depending on the input numbers!, if so where will they go the noise and uncertainty?