why in oscillator circuits with only a DC source the capacitors and inductors don't reach a steady state where the first is an open circuit and the second a short circuit (so the whole thing behaves like a DC circuit).

One can certainly design circuits that reach a steady state, where capacitors act like open circuits, and inductors like shorts. However, because they reach a steady, non-oscillating state, they are, by definition, not oscillators.

On the other hand, there is no general answer why oscillators don't behave that way, because there is no general oscillator. There are many different oscillator topologies, and your question does not specify any circuit in particular to analyse.

if the transistor were to always maintain a single state (i.e. Forward Active) then indeed the circuit would have reached a simple DC steady state (no oscillations after steady state is reached).

No, an oscillator does not require leaving the Forward Active mode in order to operate. Rather it is necessary that at some frequency, there is a gain of exactly one. This can be achieved in a variety of ways. One method, that is perhaps not so common now is to control gain via an incandescent lamp as a feedback element. As oscillations increase, the lamp heats up, and gain is reduced. Another method is to make use of a diode's non-linear characteristics to achieve gain control.

I do wonder if as far as it goes, the statement above is valid

An oscillator may be designed to use transistor saturation as part of it's overall mechanism. But it is not required that all oscillators behave this way.

why doesn't [a Colpitts oscillator] reach DC steady state regardless of what voltage pattern is produced as it oscillates.

There is a possible state in which a Colpitts oscillator could possibly be static. However, this state is meta-stable. That means that although it is stable, it is stable in the same way that a ball balanced on the point of a pyramid might be stable. Even a tiny disturbance will cause the ball to become unstable. Similarly, for the Colpitts oscillator. Any noise, and the oscillator will begin to oscillate. The reason is that the Colpitts oscillator, like many sine wave oscillators, is designed to have a closed loop gain greater than 1 for small oscillations, but that closed loop gain decreases to 1 as the oscillations increase to the designed oscillation amplitude. So, what begins as a very minute oscillation grows and grows until the oscillator reaches a steady oscillation.

Once it has begun oscillating, it would never approach the meta-stable state, because any decrease in the oscillation amplitude increases the closed loop gain.

why in oscillator circuits with only a DC source the capacitors and inductors don't reach a steady state where the first is an open circuit and the second a short circuit (so the whole thing behaves like a DC circuit).

One can certainly design circuits that reach a steady state, where capacitors act like open circuits, and inductors like shorts. However, any circuit, in such a steady, non-oscillating state is, by definition, not a working oscillator.

On the other hand, there is no general answer why oscillators don't behave that way, because there is no general oscillator. There are many different oscillator topologies, and your question does not specify any circuit in particular to analyse.

if the transistor were to always maintain a single state (i.e. Forward Active) then indeed the circuit would have reached a simple DC steady state (no oscillations after steady state is reached).

No, an oscillator does not require leaving the Forward Active mode in order to operate. Rather it is necessary that at some frequency, there is a closed-loop gain of exactly one. This can be achieved in a variety of ways. One method, that is perhaps not so common now is to control gain via an incandescent lamp as a feedback element. As oscillations increase, the lamp heats up, and gain is reduced. Another method is to make use of a diode's non-linear characteristics to achieve gain control.

I do wonder if as far as it goes, the statement above is valid

An oscillator may be designed to use transistor saturation as part of it's overall mechanism. But it is not required that all oscillators behave this way.

why doesn't [a Colpitts oscillator] reach DC steady state regardless of what voltage pattern is produced as it oscillates.

There is a possible state in which a (well designed) Colpitts oscillator could possibly be static. However, this state is meta-stable. That means that although it is static or "stable", it is stable in the same way that a ball balanced on the point of a pyramid might be stable. Even a tiny disturbance will cause the ball to become unstable. Similarly, for the Colpitts oscillator. Any noise (and in electrical circuits, there is always noise), and the oscillator will begin to oscillate. The reason is that the Colpitts oscillator, like many sine wave oscillators, is designed to have a closed loop gain greater than 1 for small oscillations, but that closed loop gain decreases to 1 as the oscillations increase to the designed oscillation amplitude. So, what begins as a very minute oscillation grows and grows until the oscillator reaches a steady oscillation.

[If the Colpitts oscillator is not well designed, it may have difficulty starting up, and require a "kick" to get it started. This would be due to it having insufficient closed loop gain at low amplitudes.]

Once it has begun oscillating, it would never approach the meta-stable state, because any decrease in the oscillation amplitude increases the closed loop gain.