Why a Random Reward in One-step Dynamics MDP?
In general, $R_{t+1}$ is is a random variable with conditional probability distribution $Pr(R_{t+1}=r|S_t=s,A_t=a)$. So it can potentially take on a different value each time action $a$ is taken in state $s$.

Some problems don't require any randomness in their reward function. Using the expected reward $r(s,a,s')$ is simpler in this case, since we don't have to worry about the reward's distribution. However, some problems do require randomness in their reward function. Consider the classic multi-armed bandit problem, for example. The payoff from a machine isn't generally deterministic. 

As the basis for RL, we want the MDP to be as general as possible. We model reward in MDPs as a random variable because it gives us that generality. And because it is useful to do so.