Why is dark energy preferred to the cosmological constant?
A cosmological constant should be considered a special case of dark energy. The effective stress-energy tensor for a cosmological constant is proportional to the metric $g_{\mu\nu}$, so in a local inertial frame will be proportional $\mathrm{diag}(-1,+1,+1,+1)$. This is equivalent to perfect fluid with energy density and pressure directly opposite one another, but more importantly, it is the only possible form for the stress-energy that would give the exact same energy density and pressure in all local inertial frames.

If by 'dark energy', we understand it to mean all the contributions to stress-energy in the above form, then there is no reason for this to be constant, and plenty of reasons why it might not be, as this situation is not exceptional in fundamental physics. For example, there could be false vacua with various different energy densities, and they must be invariant across inertial frames. 

In particular, the basic idea of inflation considers a flat FRW universe with expansion driven by a scalar field $\phi$ at a local extremum of its potential, $V'(\phi_0) = 0$, which yields an exponential expansion with constant energy density $T^0{}_0 = V(\phi_0)$. More refined models, such as slow-roll inflation, could therefore be directly interpreted as a time-varying dark energy density, while eternal inflation would also include spatial variability. There's plenty of other inflationary models besides.

One the interpretational flip-side, one could always have a $\Lambda$ that corresponds to the energy density of the true vacuum, and the rest as separate contributions on top of that. It's just not as useful in a cosmological context compared to grouping all 'dark energies' together, as all stress-energy gravitates equally.