The central complaint is unfalsifiability. For almost any chart, several valid counts exist simultaneously, and when price invalidates the preferred count an alternate is promoted. A framework that can accommodate any outcome after the fact makes no testable claim in advance.
A second objection is that wave structure resembles what you would expect from any series with trends and reversals. Randomly generated price series can be counted in waves just as convincingly, which suggests the pattern may be in the observer rather than the data. See random-walk-hypothesis.
None of that makes the framework useless. It gives traders a disciplined way to think about proportion, alternation and where a view is wrong. But it should be described as a lens, not as a forecasting method, and claims about specific future price targets deserve scepticism.
Related: elliott-wave-theory, random-walk-hypothesis, overfitting, technical-analysis, self-fulfilling-prophecy