Of course the potential consequence of the spiritual Fall could be even more devastating that the first death. For both consequences of the Fall, however, God had an answer, and that answer was the plan of redemption. Both the temporal and spiritual deaths would have a solution in the mission of the Atoning Messiah. However, while the temporal death had an automatic solution, the redemption from the effects of agency required even more exercise of agency.
God gave Adam and Eve commandments, "that they should not do evil." What Alma is telling us is that after God imposed the conditions of the Fall, he taught Adam and Eve what they needed to do to be redeemed. The first is that they should eschew evil. Now that man knew the difference between good and evil, God made sure that man knew that he wanted us to do good, and not do evil.
It is too easy to assume that it would be obvious to Adam and Eve that they should do good and not evil. We expect that since we use the terms good and evil that they immediately understood that good was, well, good. What the knowledge of the Gods (knowing good from evil) did was to institute the ability to discern differences. Knowing which of those different things was the right one to chose is not obvious to from the choice itself. God's commandments tell us it is right.
For example, is it good to steal? It is quite possible that one might think that it is. If you steal, you end up with something that you wanted, and you get it for free. Surely getting something you want for free is good? Isn't stealing very close to getting a gift? In both cases you get something for free.
The difference is that God tells us that stealing is evil. Therefore when we are faced with the decision, we can know which option is good and which is evil. Even though we might see some good things coming from the theft, we yet know that it is evil. Nevertheless, this is something that we must learn, and the fact that so many in the world chose to steal tells us that the choice between good and evil is not necessarily obvious. When we see a power saw, we have a rather quick realization that sticking our hand in it so that it is cut off is not a good thing. Most of the ways in which we exercise our agency are not nearly so well defined. Most of them really do have ways in which both sides of the issue can seem "good." In those cases, it is God who provides the ultimate definition. He did this from the beginning through the commandments.
Rhetorical: Alma concludes this part of the argument my defining the doing of evil as the second death. The consequences of choosing to do evil (and not repenting) is that one will stand before God in one's sins, and justice will require the exclusion from God. At this point he has not yet begun to emphasize the redemption of sin. In the way he is building the argument, it is more important to emphasize the extent of the problem first. The reason he adopts this particular mode of reasoning is that he is speaking to a group of people who do not accept this part of the redeeming mission of Christ. Thus he must clearly set up the need for the redemption from sin, precisely because this is a people who do not believe in a Savior from sin.