Using an external Pattern breaks Format

Question

I noted while writing this answer that using an external Pattern on Format doesn't work:

p : Format[_foo] := bar

foo[1]

foo[1]  (* did not work *)

The FormatValues reflect the definition:

FormatValues[foo]

{HoldPattern[p : _foo] :> bar}

However the definition is not in the correct form. Compare the one without Pattern:

ClearAll[foo];  Format[_foo] := bar;  FormatValues[foo]

{HoldPattern[MakeBoxes[_foo, FormatType_]] :> Format[bar, FormatType], 
 HoldPattern[_foo] :> bar}

Note that here the rule is rewritten in terms of MakeBoxes

foo[1]

bar  (* it works now *)

Is this behavior a bug or is there a reason for Pattern to prevent the standard rule formation?