The term "functional load" goes back to the days of the Prague School; references to it can be found in the work of Vilém Mathesius in 1929.
Its most vocal advocate was André Martinet, a historical linguist who claimed it was a factor in the likelihood of a phonological merger.
[1] The first suggested measurement for functional load was the number of minimal pairs, but that does not take into account word frequency and is difficult to generalize beyond binary phonemic oppositions.
There are innumerable sets of words distinguished just by their vowels, such as pin, pen, pan, pun, pain, pine.
The distinction is fully maintained in nearby Australian English, where many find comedy and confusion in mergers such as sheep-sharing vs. sheep-shearing.