Well, well. A 13 includes b7, 9, 11, yes, but the main sound you want is the major 3rd, and the tension between b7 and 13. The 9th and 11th are usually omitted. (And on a side note: if you want the 11 in there, use 13sus to replace the 3rd). The main point of a b13-chord is the dissonance between the 5th and the b13. If you don't want the perfect 5th, write + (or #5) to indicate a raised 5th instead of using b13.This is WRONG. When notating extensions on a chord symbol, it implies all the extensions below by default. It is up to the musician to understand and voice properly by omitting the dissonance between the third and the eleven or the fifth and the b13 for example. BTW the major 7th IS NOT a dissonance but the minor ninth interval IS a dissonance and that IS the reason why we should avoid having a major third and an eleven within a chord.
That is why it is important to understand the theory behind chord construction and their harmonic functions. We shouldn't have to indicate a symbol like this: C13(add9, no 11) for example