My 1949 shower floor is missing grout, although I've never seen any signs of leakage on the ceiling below...

So, couple questions. How the hell is nothing leaking with this much grout missing?

Should I make an attempt to clear out the rest of the grout and give it a nice re-grouting or just leave it alone? If re-grout, do I use caulk where the green meets the black curb?