Why would we have roaches in here?

Roaches make meals of lots of things that we don’t consider to be “food”. They – and other insect pests – go for cardboard, the paste that holds cardboard containers together, and the glues used in postal envelopes, to name a few.

A lot of sailors in tropical climates, for example, won’t bring anything onto the boat that’s in cardboard, or which hasn’t been first dunked in seawater to ensure that insects and other pests will vacate it.

Without knowing more about the contents and construction of your mailbox – and maybe your climate, too – it’s not possible to be much more specific than that.

It could also just be a dry place that offers shelter while they forage for food elsewhere.

The one clear imperative when spotting a cockroach on or near anything that is going to wind up in your house or vehicle is to understand that hostilities have commenced and you are on the defensive! Do the research, and begin mobilizing NOW. There is no time to lose!

Are they roaches or are they Earwigs???

I thought roaches like water. Is water getting in the mailbox?

Protection.
They are out of the elements, and predators can’t reach them.
In such a small, confined area, they shouldn’t be too difficult to get rid of. I urge you to do so before, as @stanleybmanly points out, they migrate to your house via the mail.

There are spiders nested in my mailbox, year after year, but I don’t mind.

I agree with @CWOTUS. While you might not consider the contents of your mailbox to be food, the gum on envelopes and the like are tasty to cockies. Ugh. I hate cockroaches. Do your cockroaches fly?

Storage lockers, too, are pest magnets.
The battle for mice and roaches – and almost all the other pests that infest our houses – is shelter. Both will eat, literally, almost anything if they live long enough to breed. It’s likely that the roaches in your mailbox are wood roaches that eat decayed, wood, but they’re very adaptable and it’s better not to take the chance.

I have some sort of telephone junction in the corner of my front yard. Looks like a plastic tube, about 36” tall and 8” around. Apparently it’s just the shelter the field mice need. About once a year the phone line gets static and the phone company comes to clean out the nests and replace the nibbled wires.

@ibstybro all the mailboxes around here are metal boxes on big, hand laid brick.
@Earthbound_Misfit no; I’ve not seen any fly yet, thank God.
@JLeslie it could be that some rain is getting in the seams of the metal box, yes.
@Tropical_Willie they are definitely roaches. Disgusting.

Individual, stand-alone boxes, @Aster?

If so, it may be overkill, but if I were you, I would get a Raid Fumigator and a garbage bag large enough to cover all or most of the box and post to the ground.
Early on a Sunday morning, activate the Fumigator and put it in the mail box. Leaving the door open, cover as much as you can with the trash bag and tie at the bottom. Uncover after the recommended amount of time. There is no clean-up or residue with the fumigator. For good measure, you might sprinkle some insect powder – like Seven – around the base of the box while it ‘cooks’.

I would be amazed if you ever see another roach.

They fly here. Makes it harder to keep them out and they can be big.

I hate when you open an undisturbed drawer and see one scurrying away. Enough to dispel all Buddhist tendencies and send me into a baygon spraying fugue.