Which of the five senses is the most studied in terms of memory and why?

More than any other sense, the sense of smell is the sense that is most closely tied to memory; however, scientists do not have definitive reasons for why this is. Scientists know that the connection between memory and smell is stronger than memory and other senses, but there are competing theories that attempt to explain the correlation. A leading idea deals with where the sense of smell is processed in relationship to the rest of the brain. The olfactory bulb is in charge of processing smells, and it is located right next to the hippocampus. Scientists have identified the hippocampus as an important piece for creating new memories for events. Scientists suspect this proximity has something to do with why smell and memory are so closely tied. Additionally, the brain processes smell differently than any other sense. The pathway into the brain for the other four senses starts at the sense organ and then moves to the thalamus before going on to the rest of the brain. The thalamus acts as a relay station of sorts. Smell bypasses that relay station.

Rather than visiting the thalamic relay station on its journey into the brain, smell information travels directly to the major site of processing—the olfactory bulb—with nothing in between. We do not know what stopping off at the thalamus does for the other senses, but it certainly means that signals generated in the other senses are somehow “further away” from the nexus of processing done in the brain.
https://www.bbc.com/future/article/20120312-why-can-smells-unlock-memories

https://www.psychologytoday.com/us/blog/brain-babble/201501/smells-ring-bells-how-smell-triggers-memories-and-emotions