Does item homogeneity indicate internal consistency or item redundancy in psychometric scales?

The term 'internal consistency' has been used extensively in classical psychometrics to refer to the reliability of a scale based on the degree of within-scale item intercorrelation, as measured by say the split-half method, or more adequately by Cronbach's (1951) (Psychometrika, 16, 297-334) alpha, as well as the KR₂₀ and KR₂₁ coefficients. This term is a misnomer, as a high estimate of internal item consistency/item homogeneity may also suggest a high level of item redundancy, wherein essentially the same item is rephrased in several different ways.