It is always possible that experience of bad economy service may push some pax into a premium class. But the number of pax that this applies to will be tiny. If you provide bad economy service, you are much more likely to drive pax to competing economy classes - including the low-fare competition, on those routes that have it.
But compare legacy carrier with a low-cost.
If a legacy drives passengers away from their economy, then most go to competing economy classes, including low-fare competition, or do not fly, and only a few go to premium classes.
If a low-cost drives passengers away from their economy class, all of them go to competing economy classes, including those of other low-costs, or do not fly at all. None of the passengers driven away from the economy service of that low-cost go to premium service of the same airline, because the low-cost does not have any.
Therefore, low-costs should also be unable to afford driving passengers away.