The 16 ga was supposed to cover the gap between 20 ga and 12 ga. It was considered a good light weight field gun because many were built on a 20 ga frame, and packed almost as much payload as a 12 ga. It overlapped the performance of the two gauges on either side of it. This was a big selling point 75-100 years ago. But you can't deny physics, so the 16 ga guns tended to kick more than either a 20 ga or a 12 ga, light weight and heavier payload mean more felt recoil. But many, many people liked the light weight and pointability of the 16 ga guns.
Fast forward several decades. When the 20 ga 3" magnum was introduced, the 16 ga was doomed. The 3" 20 could launch a heavier payload than the 16 ga, as heavy as many 12 ga field loads. WW2 and post-WW2 manufacturing standardizing designs and simplifying manufacturing meant something had to go, that meant the overlapping 16 ga was out. Since 12 ga and 20 ga were competition gauges, gas-operated semiautos became available for them, and not for the 16 ga. When replacable chokes were introduced in 1983, the 16 was left out again due to limited numbers of guns made for it. After about 1986, the 16 ga got another nail in the coffin, steel shot was required for waterfowl in many areas and was not available for the 16 ga, and older guns with thinner barrels could not shoot it anyway. So now the 16 is a relic of days gone by, barely hanging on but not totally gone like the 14 gauge and the 24 gauge. Every now and then some gun rag writer will rediscover the magical qualities of the 16 ga and excite a few people, but it happens less and less frequently.
