One of the reasons a straw is just as strong as a wooden dowels is because when it is pushed in to the cake the displaced cake is INSIDE the straw, thus not distorting the basic structure of the cake tier. With a wooden dowel the displaced cake is pushed sideways and up around the dowel with the possibility of distorting the tier. Now the straw may be plastic but it is thicker, wider and stronger than a normal straw and has a larger surface area around which to bear the weight of your cake tiers.
No matter what sort of support you use for a cake, if it is going to slip and slide and the cake tiers fall off, they will!! I have seen cakes using wooden dowels fall over. This happens due to a number of reasons, least of which is the type of support inside the tiers.
I have used both types of supports and much prefer the straw for each individual tier. However, a central support rod/dowel for the entire structure may well have to be a wooden rod just for the height aspect as straws aren't made very tall!