When your buddy says "if you dont get instructions fly the missed" is that because he's thinking about the pilot must act like radios are out without comms? This isn't a hanger talk example, you have to get clearance to fly the published missed or get their headings and alts. What I didn't realize, and i would guess many of our pilots at my company didn't realize, is tower formalizes all those missed procedures and we don't have a good indication in the chart of what that is.
NY has had it happen too, which is why it was an area of focus, but MSP has a hardly used runway which when they go to that single runway op, the missed approach puts you into downwind ifr traffic. Our guys have done it.
You need to be cleared to go missed, and if your radio is working, continue climbing to your flaps retract altitude until you get that clearance. In the runway 31L example the place you must turn is 6 miles beyond the end of the almost 3 mile long runway.
Added in post: Both NY towers have formally made their position clear on this matter to my company. Don't go executing the published missed unless you get clearance for it. To re emphasize, this is a normal, vanilla approach, don't go down rabbit holes ofZOMG now the radios don't work too and the engine is on fire and the other is shut down.