When Jesus said disciples are to be the salt of the earth, he wasn't talking about flavor or preserving.
He was talking about dung and ovens. Interpretations of preserving and flavor really do not capture the picture of a believer's calling. It's a different challenge...
Several Bible scholars have noted how a single Hebrew word can stand for a larger phrase or idea. In Psalm 12:6 and Job 28:5 the word "earth" stands for "earthen oven." The context about refining metals and baking bread help reinforce this meaning. Job even mentions the fire of the oven. (He's not talking about the earth's hot magma.)
Likewise, the context of Matthew 5:13 indicates Jesus was talking about an earthen oven. Believers are to be the "salt of the earthen oven." Ovens need fuel and while there was not ample amounts of wood for fuel in ancient Palestine, there was plenty of donkey, camel, and cow dung. Fresh manure was mixed with chaff (Isaiah 25:10 even notes this) and salt to dry and form the dung into patties then dried further in the sun. The drying effect of the salt helps the dung burn hotter and brighter because energy is not wasted evaporating moisture out of the fuel.
Salt plates or chunks were placed in the bottom of earthen ovens to also facilitate the fire. Eventually, the salt in the oven would wear out and need to be replaced. When Jesus says we are the salt of the earthen oven, it means we are to facilitate fire in the oven. Ovens were used to refine metals and bake bread. Bread is associated with life-giving sustenance. Further, in the ancient metaphors of reality, fire was associated with life. Living beings have "fire" in them and fire gives off light (Matthew 5:14-16). All of this imagery played together for Jesus' audience.
In other words, followers of Christ are to stoke the fire of life, the gospel. This will give life to others just as the fire in an oven provides bread for others. The life (fire) is the gospel and kingdom of God. Proclaiming the gospel by words and good works (v. 16) shares this light with others and it should never be hidden.
If the salt in the oven becomes useless (1), it has no purpose and must be cast out. It became trash and in ancient villages, trash (even sewage) was thrown out into the street where it was trampled by people. God's kingdom doesn't have trash! A person is not follower of Christ if they do not live according to their purpose, which is to facilitate the life-giving fire of the gospel by what they say and do (2).
Are you living according to your purpose? Are you intensifying the life-giving fire of the gospel so it can burn brighter and hotter for others?
1. The Greek word we translate as becoming "tasteless" is most often translated as "foolish" or "useless" in ancient documents and in Romans 1:22 and 1 Corinthians 1:20.
2. The reason "flavoring" and "preserving" are not the best metaphors is primarily that these ideas do not fit the context of Matthew 5:13-16. Secondly, this is a fallen world. The Epistle of Romans makes it clear, as does Ephesians 2:1-3, that apart from Christ people are "dead." The dead do not need preserving or flavoring, they need life. God does not intend to preserve or flavor a fallen world, but re-create it through Christ (Romans 8:18-23). Therefore, the expression "the salt of the earth" is not about being humble and unpretentious. It's a litmus test distinguishing Christ's followers from unbelievers.
The scholars and sources helpful to this are Bruce Malina, The New Testament World: Insights from Cultural Anthropology (2001); John J. Pilch, "Salt for the Earthen Oven Revisited," HTS 67:1 (2011); Bruce Malina & Richard Rohrbaugh, Social Science Commentary on the Synoptic Gospels, (1992).