You haven't answered the questions.
I don't see a reason to use RDBMS in a browser, if it's not, for example, an SQL tutorial site.
You gave an example of a t-shirt store. A plain array of JS objects is enough to store items in a browser. Why do you need a fully backed RDBMS for it?
Sorry, but it's just you opinion. Do you have proofs of how t-shirt store will benefit of putting RDBMS on a client side (how much space does it take BTW) instead of using simple list of objects?