Peppers, like a lot of modern veggies (especially beans/peas), are pretty much extreme mutants compared to their ancient/wild counterparts.

We've selected them over 1000s of years to grow fruits/pods/etc that are extremely larger than they need to be in order to survive and be spread in the wild. While large, fleshy, peppers/toms/eggplants/etc are great for humans, all the plant cares about from a survival standpoint is having enough flesh on them that an animal attracted to them will eat them and poop them out...or otherwise disperse the seed.

Along with the mutated-sized fruits...well, the flowers have also become a bit mutated in how they work vs. how they're expected to work if they were uncultivated over 1000s of years.

A lot of peppers self-pollinate rather easily when the flowers first open within a manner of minutes to hours (if they're not already self-pollinating themselves as their flowers open). This is actually an evolutionary disadvantage...but with the domesticated human crops we've selected and kept in production these mutants ceased to act like their ancient/wild counterparts long ago. In the case of many beans and peas, they self-pollinate before the flowers even fully open.

Long story short, it's quite common for peppers not to cross pollinate very easily, though they have all the proper parts to do so.

I have saved seed from many, many pepper plants that were grown in close proximity to peppers of different varieties. I have yet to replant any of the saved seed and find a cross. I have however, gotten seed from other sources that was obviously a cross or possibly just mislabeled.
I only take steps to isolate plants that I want to ensure purity on. But that is just one or two a year usually.
Bruce

My jalapeno/banana cross is looking like a corked banana pepper. I have never seen a banana pepper cork.

Nice explanation nc-crn!

I have a cross from a jalapeno and cayenne. It has the length and shape of a cayenne and the width of the jalapeno.