Australia has been using a much more complicated ranked system since 1918, and Ireland has used an even more complicated weighted proportional system. The entire state of Maine adopted IRV, and cardinal systems are much simpler. It’s not a fatal disadvantage.
The Approval Voting system is arguably simpler than the status quo, because you remove a rule. The one that stays your vote is invalid if you vote for multiple candidates.
Maybe “near-fatal” is too strong a word, the comment I replied to also had examples. Existence of examples doesn’t distinguish winning from survival, seeing some use. I understand the statement I replied to as meaning something like “In 200 years, if the world remains mostly as we know it, the probability that most elections use cardinal voting methods is above 50%”. This seems implausible to me for the reasons I listed, hence the question about what you actually meant, perhaps my interpretation of the statement is not what you intended. (Is “long run” something like 200 years? Is “winning” something like “most elections of some kind use cardinal voting methods”?)