I haven't used it before, but isn't that a statistic related to repeated measures ANOVA. If so, repeated measures ANOVA is pretty antiquated, in that multilevel modeling can do the same thing and handle missing data, which repeated measures ANOVA cannot. This may make that use of Hotelling stat obsolete.
I suspect that the OP means Hotelling T2 control charts. My understanding is that they are a multivariate control chart that is intended to provide a signal if any one or combination of variables changes in a process.
I have never used them, and am only aware of them on a theoretical basis. Based on that minimal understanding, I can envision a few drawbacks. The first would be the complexity of the chart is greater than the understanding of the intended users of the chart. You would have to have a highly trained specialist maintain the chart whereas most charts are intended to be used by the operator of the process. Second, when the chart signals an out of control condition, you would need a secondary means of determining the variables that are responsible. The primary value of any control chart is in providing fast feedback to allow a fast response.
I view it as a theoretical curiosity that is of very limited practical value when applied.