Does anyone normally advise for the metal threshold at exterior doors to be caulked? I don’t see it done very often but at my home it wasn’t done and caused some significant subfloor damage with heavy rain.
What is important is what are your thoughts and what do you base them on?
It would depend on the threshold manufacturer and if they followed instructions for its installation. One requirement is to place a bead of caulk under the sill pan before installation which is there to help seal it. Having said that you can bet most if not almost all are not installed per the manufacturer requirements. And since we can’t see if they did it right I do report it and recommend that it be sealed to prevent issues.
I do report it and recommend sealing them to help extend their life.
Hard to tell from your picture but there are indications they might have covered the flashing with a shingle(s) for aesthetic purposes. Were there others like this?
That is called experience. You were paid for that experience regardless if it happened on your home or someone else’s. If you think a bead of caulk should go there, call it out with confidence based on your experience.