  In this work we study the role of parasitic interactions and microwave
crosstalk in a system of two superconducting artificial atoms interacting via a
single-mode coplanar waveguide. Through a general description of the effective
dynamics of the atoms, beyond the two-level approximation, we show that the
atom selectivity (ability to individually address an atom) is only dependent on
the resultant phasor associated to the drives used to control the system. We
then exploit the benefits of such a drive-dependent selectivity to describe how
the coherent population inversion occurs in the atoms simultaneously, with no
interference of residual atom-atom interaction. In this scenario the parasitic
interaction works as a resource to fast and high fidelity control, as it gives
rise to a new regime of frequencies for the atoms able to suppress effective
atom-atom coupling (idling point). To end, we show how an entangling $i$SWAP
gate is implemented with fidelity higher than $99\%$, even in presence of
parasitic interactions. More than that, we argue that the existence of this
interaction can be helpful to speed up the gate performance. Our results open
prospects to a new outlook on the real role of such ``undesired" effects in a
system of superconducting artificial atoms.
