When planning out my programs, I often start with a chain of thought like so:
A football team is just a list of football players. Therefore, I should
It depends on the behaviour of your "team" object. If it behaves just like a collection, it might be OK to represent it first with a plain List. Then you might start to notice that you keep duplicating code that iterates on the list; at this point you have the option of creating a FootballTeam object that wraps the list of players. The FootballTeam class becomes the home for all the code that iterates on the list of players.
It makes my code needlessly verbose. I must now call my_team.Players.Count instead of just my_team.Count. Thankfully, with C# I can define indexers to make indexing transparent, and forward all the methods of the internal List... But that's a lot of code! What do I get for all that work?
Encapsulation. Your clients need not know what goes on inside of FootballTeam. For all your clients know, it might be implemented by looking the list of players up in a database. They don't need to know, and this improves your design.
It just plain doesn't make any sense. A football team doesn't "have" a list of players. It is the list of players. You don't say "John McFootballer has joined SomeTeam's players". You say "John has joined SomeTeam". You don't add a letter to "a string's characters", you add a letter to a string. You don't add a book to a library's books, you add a book to a library.
Exactly :) you will say footballTeam.Add(john), not footballTeam.List.Add(john). The internal list will not be visible.