First I'd recommend you read the answer to the question the OP mentions to understand LDS belief on Adam and Eve or this Ensign article.
In answer to your question, yes and no the LDS believe subsequent events as somehow necessary on the larger scale of things.
The reason why evil people can do evil things is because of agency:
[which] is the ability and privilege God gives us to choose and to act for ourselves. Agency is essential in the plan of salvation. Without agency, we would not be able to learn or progress or follow the Savior. With it, we are “free to choose liberty and eternal life, through the great Mediator of all men, or to choose captivity and death, according to the captivity and power of the devil” ( 2 Nephi 2:27).
...
The Lord has said that all people are responsible for their own motives, attitudes, desires, and actions. Even though we are free to choose our course of action, we are not free to choose the consequences of our actions. The consequences, whether good or bad, follow as a natural result of any choice we make.
(this doesn't mean the LDS condone atrocities)
People can also choose instead to serve others, follow God's commandments, etc.
Man purpose isn't to experience pain or to do evil. From 2 Nephi 2:25 we know that:
25 Adam fell that men might be; and men are, that they might have joy.
Later in 2 Nephi 9:25,35 it says:
25 Wherefore, he has given a law; and where there is no law given there is no punishment; and where there is no punishment there is no condemnation; and where there is no condemnation the mercies of the Holy One of Israel have claim upon them, because of the atonement; for they are delivered by the power of him.
35 Wo unto the murderer who deliberately killeth, for he shall die.
Overall 2 Nephi 2:13 summarizes that yes bad things happen but we know they are bad because of the law. We know sadness because of happiness, if we only had good things happen all the time we wouldn't be happy because we wouldn't have known sadness.
13 And if ye shall say there is no law, ye shall also say there is no sin. If ye shall say there is no sin, ye shall also say there is no righteousness. And if there be no righteousness there be no happiness. And if there be no righteousness nor happiness there be no punishment nor misery. And if these things are not there is no God. And if there is no God we are not, neither the earth; for there could have been no creation of things, neither to act nor to be acted upon; wherefore, all things must have vanished away.
See also The Purpose of Earth Life
Read 2 Nephi 2 to get a better answer about the Fall, agency, and overall a better answer then what I attempted here