Not so for modern cables, as far as I am aware. In fact, the grease can be an inhibitor in shifting. The plastic liner on the standard Shimano outers and the stainless steel cables take care of the anti-friction needs. Grease only if you are installing galvanised wire in unlined outers -- which is very definitely unlikely in this case.

I use the Dura-Ace cables that come only in silver outers. It's about all I can afford that is of Dura-Ace level.

Breakages of the mushroom tip from the end of shifter cables are not so unusual. I have had probably four go in around 86,000 accumualted km in the past 10 years. Two were on MTB shifters, and two have been on Tiagra shifters. The diameter of the little pulleywheel inside the shifters that pulls the cable is quite small, and the end of the cable almost needs to kink to get round it.

Regular replacement is the solution. And it all depends on how far you ride a year. If your bike does 2000km, maybe once every two or three years; if it does 16,000km, replace them every year or even more often.

As to other cables -- the brake cables are beefier and the mushroom is larger in proportion. The stresses are somewhat less on the ends of the brake cables because they are more a direct pull than a wrap-around pull like on the shifters. So, they should last quite a bit longer, provided you use cable ends at the brake ends. I probably run up to 10,000km on my most-used bike before thinking about brake cable replacement.