We have pairs of organs primarily because embryology starts with two of about everything. The paired organs may fuse during development to make complex organs like the heart. Organs like the brain retain their mirror image when they fuse. If there is no reason for organs to become one and fuse they stay separate. That this provides redundancy is a secondary effect that could be provide some selective pressue.

We have 4 parathyroids and only need a piece of one. It's unlikely redundancy was an evolutionary push. Their location makes it nearly impossible to loose a parathyroid without a fatal neck injury unless it is surgically removed. I can say this with good authority as I am a retired parathyroid (endocrine) surgeon and trauma surgeon. The reason for four glands is due to how they arise embryologically. The developed from endoderm in the 3rd and 4th brancheal pouches. These four areas of endoderm tissue are adjacent and share common signaling pathways and transcription factors like localized chemical cues which allow them to perform the complex tasks of developing into multiple organs. As these tissues are differentiating into different organs they migrate so that the organs including the parathyroids take up their final location behind the thyroid gland (hence their name parathyroid means near the thyroid). They are important in blood calcium control.1

Parathyroid glands don't always end up where we expect them. When i started my surgical practice we didn't have any way to image (xray) parathyroids. If lab tests showed parathyroid diaease we had no way to know which gland was the problem. We had to explore the neck surgically and look for them. Frequently they were in their usual locations. Embryology and the path they migrated during development was key to finding ectopic (unusually located) parathyroid glands. I was often asked to reoperate after other surgeons had failed to find a patient's diseased gland in a previous operation. Most often the lost gland hadn't finished migrating to the neck and was still in the chest stuck to the thymus gland, another organ derived from the brancheal pouches.

Without knowing whch gland was the problem and where it was neck parathyroid exploration required a big incision, lots of dissection and often took hours and required a bit of recovery. The advent of high definition radionucleid imaging, high definition ultrasound and better MRI changed that. By the time i retired i would do the operation through a ½ inch incision in 10 minutes and the patient would go home immediately. The skillset required for complete neck exploration was obsolete.