Actual standing waves have nothing to do with causing the output device in a transmitter to fail, in fact it's the reverse or reflected current which helped to create the standing waves which is flowing into the output device that causes the failure, is this true ?
If we say there is a standing wave on a feed line, we are saying that the voltage and current along the length of the line have a certain shape in space and over time. But the transmitter doesn't care about any part of the line except the part it's connected to.
You can use the idea of standing waves to help understand and calculate how the end of the line at the transmitter will behave — and in particular, it matters what phase the reflections have, not just that there is reflected power at all — but once you have your answer in terms of current and voltage over time at that point that's all that matters, not what it might be some distance down the line.
This is a bit like saying, "it's not the fall that kills you, but the sudden stop at the end."
Technically, it's not the standing waves per se that cause the damage. However, standing waves imply a mismatched load possibly outside the transmitter's specifications, which implies a potential for excessive heating or voltage in the transmitters, which can lead to damage. Therefore, standing waves imply a potential for damage, even if they aren't the direct cause.
Standing waves are not what causes the damage.
Heat buildup in the transmitter from accepting some of the reflected power may cause the transmitter to overheat.
But tubes are typically less vulnerable to this and can withstand a higher SWR, and solid state devices typically drop power until the heat buildup is not an issue. Also, it is possible to block the incoming power so the transmitter is not affected. (For instance, a tuner can do this.) Under these conditions, swr around 10 might be acceptable.
Another reason we avoid high swr is to avoid inefficiency. If you have high swr in a feed line with less than perfect efficiency, it will absorb some fraction of the power on each bounce (and heat up slightly) and this will result in less transmitted power. This power drop may or may not be a concern depending on the power level and the feed line efficiency.
But if you have a transmitter that is able to reflect the power back, and transmission line (like windowed ladder line) that is low loss, then the high swr is less of an issue, and eventually the reflected power will reflect again and get into the antenna (perhaps after several reflections). The reflections themselves might cause issues (like ghosting) if the frequency is high enough or the feed line long enough, but at HF this is usually not an issue.