I am a little bit confused why Find
(for example) isn't available on the
IList which List inherits from.
While I'm not privy to the decision process of the designers, there are a few things they were probably thinking.
1) Not putting these methods on IList keeps the intent of the contract clearer. According to MSDN, IList "Represents a collection of objects that can be individually accessed by index." Adding Find would change the contract to a searchable, indexable collection.
2) Every method you put on an interface makes it harder to implement the interface. If all of those methods were on IList, it would be much more tedious to implement IList. Especially since:
3) Most implementations of these methods would be the same. Find and several of the others on List would really be better placed on a helper class. Take for example, ReadOnlyCollection, Collection, ObservableCollection, and ReadOnlyObservableCollection. If I had to implement Find on all of those (pre-LINQ), I would make a helper class that takes IEnumerable and a predicate and just loop over the collections and have the implementations call the helper method.
4) LINQ (Not so much a reason why it didn't happen, more of why it isn't needed in the future.) With LINQ and extension methods, all IEnumerable's now "have" Find as an extension method (only they called it Where).