I have read a paper about "approximated decomposition" of a unitary single gate (Solovay-Kitaev algorithm) which told us a any unitary single gate can be decomposed into {Hadamard, Phase} with any accuracy $\epsilon$ . The number of {Hadamard, Phase} grows exponentially as the $\epsilon$ becomes lower and the result is a better approximation of the gate. However, in simulator or emulator such as project Q and Qiskit, the $U3$ gate seems exacted decomposition which means only one parameterized $U3$ gate can realize any unitary single gate.
So if we can realize "exact unitary single gate" in quantum computer, why still so many people focus on the "approximated one" and try to optimized the sequence after decomposition?