The reason that a Moly rich grease is recommended is that moly works in a way that grease can't.
Especially in high heat appications like power valves. In that sort of situation the oil will fall out of suspension with the soap base. If there were nothing else in the grease, this would be the end of the greases ability to protect the metals. However, with a moly rich type of grease, the molybdenum disulfide molecules are distributed on the surfaces of the metals at application. Once the grease sees high temps, and the oil starts to seep out of the soap base, the molybdenum disulfide will still be there protecting the metals from wear, as the moly actually adheres itself to the metals like little microscopic magnets, and will continue to protect. This is something that multi-purpose lithium based grease cannot do on it's own.
There really is no such thing as a "waterproof grease", however, some are built to withstand emulsification (mixing of oil and water) better than others. And yes, using these type of greases is fine for linkages and other bearings, but the addition of moly is a bonus that NO grease, that does not contain any sort of barrier type additive such as moly, can accomplish.
Your best bet is to use a moly fortified grease when it is called for.