I think it is OK to say that all circuits have inductance and capacitance, if we include small parasitic effects. However, if we neglect parasitics in a circuit that is primarily non-reactive at the frequencies we are dealing with, the transient response is practically instantaneous, and practically speaking you can say that a transient response doesn't really exist since the steady state response exists alone, immediately.
One might argue that delay effects are separate from reactance from the point of view of circuit theory, and in this case the system with delay does have a transient response. However, delay effects are a manifestation of field effects, which then leads to circuit models as transmission lines, which can be viewed as distributed inductance and capacitance.
It will be interesting to see if someone can think of an exception. Essentially, you are describing a system without dynamic state variables and state equations.