Ketchup, as mentioned, doesn't spoil easily. It's laced with vinegar and salt. Essentially, it's sweet pickled liquid tomato. Are you really using this as an argument with your wife? You realize now that she'll bring up that you were wrong on this for the rest of your marriage, right? :D

We refrigerate.... out of habit I suppose but I agree most all restaurants likely do not

I always refrigerate ketchup after opening it.

Yup. Actually I like the taste of my ketchup more when it is cold.

I refrigerate ketchup and leave it out an hour before I use it.

I'm pretty sure this cycle increases the likelihood of spoilage, but I haven't had a bad stomach from it ever.

I refridgerate all relishes,chutney,sauces,condiments, etc...
As a bachelor who lives alone I often have to throw items out for non use-past expiration.
At work I go through the pantry and fridge every three months and toss things that are even close to their expiry date.I know this is a horrid waste-I sometimes do take then to a food closet-but really do poor folks want black raspberry preserves flavored with cognac,or Nutella ?

As others have pointed out, refrigeration tends to lengthen the shelf life of most products.

But any condiment that has a high degree of salt or vinegar, like soy sauce or hot sauce, doesn't have to be refrigerated.

It's more a matter of personal taste or preference than a matter of food safety.

In addition to ketchup, I also refirgerate mayos and mustards after opening them.

Either stick a knife up the bottle to help get the ketchup flow started or tilt it on an angle at whack it on the number 57