As with their language, this is a marvel of inefficiency (good luck giving directions) and makes me wonder how they accomplish so much while starting at what seems from the outside to be such a tremendous disadvantage.
I actually think it has advantages and disadvantages. An address has a neighborhood, a block number, and a house/building number. The neighborhood name puts you in the correct vicinity. There are signs showing the block numbers, though I never got the knack of finding them.
The advantage over street names is that the first part of the address, the neighborhood name, gives you a rough idea where the address is located. Knowing a street name in the US may tell you very little. Streets can and often do extend all the way across town. Older streets can zig-zag or have disconnected segments.
The disadvantage is that in the US, if you know a street name and a cross street, you can often find one of the streets by wandering around randomly. Then you can go up and down that street looking for the address or the other street. Wandering randomly in Japan is fun, but not a good way to find an address.
Another disadvantage I've encountered is that you have to be very careful of neighborhood boundaries when consulting a map. Looking for block 12, you follow the numbers across the map 8, 9, 10, 11, 12 but you don't realize that the block 12 you found is in the adjacent neighborhood, and the correct block 12 is all the way on the other side.