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No idea. It may worth noticing that though:

sage: bool(func(0) == func(0).simplify())
True

Something inside the object is modified:

sage: hash(func(0)) == hash(func(0).simplify())
False

sage: hash(cos(x)) == hash(cos(x).simplify())  
True

No idea. It may worth noticing that though:

sage: bool(func(0) == func(0).simplify())
True

Something inside the object is modified:

sage: hash(func(0)) == hash(func(0).simplify())
False

sage: hash(cos(x)) == hash(cos(x).simplify())  
True

Which may explain why the method .subs() is not able to recognize that func(0).simplify() is the same as func(0).