Example: A pikachu only knowing electric moves.
Absolutely not. Why?
Go! Diglett! Yeah. It is best to have all your moves of a different type, so you can spread out your coverage. Hidden Power [Ice] takes care of that by hitting Ground types that are immune to Electric.
Spread out the types, spread out the coverage.
No that is horrible, a type that resist your type can come in and wreck you.