Capacitors store energy, they don't dissipate it. Likewise with inductors.
Transmission lines represent both capacitive and inductive loads simultaneously. The capacitance, inductance, resistance of the transmission line together combine to form the characteristic impedance of the line. (Ok, there's one additional term: the conductance of the dielectric between the conductors. But, for high voltage transmission lines that are widely separated, this term is effectively 0.)
The characteristic impedance of a transmission line is of primary importance for determining the ideal load impedance for the line. In an impedance matched system, the maximum power will be transmitted to the load with no reflections.
Reflections can cause a phase shift between voltage and current, making a transmission line effectively look reactive or inductive. (See surge impedance loading.) This can be corrected for in the same ways as reactive or inductive loads by adding capacitance or inductance elsewhere.
If the load itself is reactive or inductive then you can get reactive power transfer. Reactive vs. inductive is in some sense a matter of sign; in one, current leads voltage, in the other current lags voltage. In both cases, current is out of phase with voltage and that's the problem to be solved.
Reactive power doesn't transmit any actual power to the load, but it still sends current through the system. Current is subject to ohmic losses (thanks to our friend I*I*R). Sending current without delivering real power subjects you to losses without any benefits.
In general, the capacitance of the transmission line itself isn't the culprit on its own. Rather, if you have a reactive load (either capacitive or inductive), or you have imperfect impedance matching between the load and the transmission line, you can get current flowing through your wires that isn't driving a load. That excess current incurs plain ol' resistive losses.
There is one way high capacitance can cause real problems for transmission line management, though. The rate of propagation of waves through a conductor slows in proportion to the square root of the product of the inductance and the capacitance. So, for a highly capacitive line, reflections move slowly through the system, and it becomes more difficult to compensate for transients. That seems to be the real bugbear for buried high-capacitance lines. Again, you're not losing to the capacitance directly, but rather to the knock on effects that lead to poorly compensated reflections and reactive power transfer in the system.
(Dr. Jetton, if you're reading this... EE305 may have been 20 years ago for me, but I haven't completely forgotten it. And Dr. Schertz... I didn't completely forget my T-line theory either. I wouldn't be surprised if either of you would point out flaws in my summary above.)