Why doesn’t the compiler convert var[] to object[] in c#?

The new [] notation is for saving you to type an explicit type of the array members (or allowing you to create arrays where its elements have an anonymous type), but its type inference is limited in that all elements must share the same type or be implicitly convertible to a common type shared by at least one member. See C# Specification, section 7.6.10.4:

An array creation expression of the third form is referred to as an implicitly typed array creation expression. It is similar to the second form, except that the element type of the array is not explicitly given, but determined as the best common type (§7.5.2.14) of the set of expressions in the array initializer.

The following are examples of implicitly typed array creation expressions:

var a = new[] { 1, 10, 100, 1000 };                       // int[]
var b = new[] { 1, 1.5, 2, 2.5 };                         // double[]
var c = new[,] { { "hello", null }, { "world", "!" } };   // string[,]
var d = new[] { 1, "one", 2, "two" };                     // Error

The last expression causes a compile-time error because neither int nor string is implicitly convertible to the other, and so there is no best common type. An explicitly typed array creation expression must be used in this case, for example specifying the type to be object[]. Alternatively, one of the elements can be cast to a common base type, which would then become the inferred element type.

Key point here is that the “best common type” can only be one of the types already present. As Damien_The_Unbeliever pointed out in a comment: “As Mr. Lippert is fond of pointing out around inference, whenever it’s looking for a best common type, it will only return one of the types that is already present – it doesn’t go hunting for the most-derived common ancestor.”.

Just because every array could be an object [] doesn’t mean it should. From a compiler perspective that’d be a trivial last-resort choice, but a very counter-intuitive one for the developer, I guess.