Correlations between observed variables tend to be underestimates of the true score correlations due to random measurement error (unreliability). You may thus underestimate convergent validity. Moreover, when observed variables have different reliabilities, convergent validity coefficients are difficult to compare across variables. Confirmatory factor analysis provides a correction for measurement error by estimating correlations among latent variables.
The major limitation is that inter-item correlations assess reliability, but reliability does not imply validity. That participants are responding consistently to a set of items does not imply those items are all measuring the same underlying construct.
According to PLS-SEM (ADANCO), Discriminant Validity could be used for the Heterotrait-Monotrait Ratio of Correlations and Fornell-Larcker Criterion.
Construct validity refers to how well a test measures the concept for which it was designed. It is essential for establishing a method's overall validity.
Assessing construct validity is particularly important when studying intangible phenomena, such as intelligence, self-confidence, or happiness, which cannot be directly measured or observed. To evaluate these constructs, multiple observable or quantifiable indicators are required.
Validity of measurement types, Construct validity is one of the four measurement validity types. The remaining three are:
Content Validity: Is the test completely representative of what it intends to measure?
Face validity: Does the test's content appear to correspond with its objectives?
Criterion validity: Do the results accurately measure the specific outcome that they are intended to measure?
Confirmatory factor analysis (CFA) is a frequent technique for determining construct validity. Similar to EFA, CFA is a tool that researchers can use to attempt to reduce the total number of observed variables into latent factors based on data similarities.
Sometimes, the high correlation among the variables happened but AVEs are over 0.5, Factor Loadings are over 0.7, SRMR is lower than 0.08 and a high explanation power model (R-square is over 0.75). Thus, it may be considered a limitation, just my two cents.