In the proof of the time hierarchy theorem given on page 69 of Arora-Barak, we define a TM D as follows:
"On input $x$, run for $|x|^{1.4}$ steps the Universal TM $\ \mathcal{U}$ of Theorem 1.9 to simulate the execution of $M_x$ on $x$." Here $M_x$ is the machine encoded by string $x$.
Since we are simulating another TM on $D$, this would implicitly make $D$ a universal TM, right? If this is the case, then why is it necessary to state that $D$ will simulate $\mathcal{U}$ in order to simulate $M_x$ when $D$ is already capable of simulating $M_x$ directly?
On the other hand, if it is not the case that $D$ is a UTM, then why can't we "run" (whatever that means) $M_x$ directly on $x$ instead of running $M_x$ through $\mathcal{U}$ (in the same way that we "run" $\mathcal{U}$)? Why do we need to simulate a machine capable of simulating an arbitrary TM if we only need to simulate exactly one TM?