I'm rather late coming in on this one, but like everyone else, can speak from experience. Being a smarty pants, I knew my times tables at age 7 and could also recognise the patterns within them, eg. that if you took the 9x lines out of all the preceding tables, and put them together you could go a long way to making up the 9x table, and so on.
I think tables are a useful tool for life and feel for those who can't relate to them. The example of the (bright) young helper dashing for his calculator is a case in point.
I did read somewhere that around 20% of adults in this country are functionally illiterate (so I'm guessing that could mean that they can't write a letter that is grammatically correct?) and even worse, 40% are functionally innumerate. Presumably that would mean they can't work with numbers at any meaningful level.
This is despite the best efforts of teachers through the years. So something needs to be done.
Tables may not enable someone to calculate the surface area of Jupiter, (no, nor me!) but they will surely be useful day to day when dealing with, eg. cash transactions. Invaluable, I'd say.