You are much better off leaving the anode in place with a full tank, as opposed to emptying the tank and leaving the anode out to try and dry the tank...
I won't go into the physics behind the corrosion process (galvanization), but, let it suffice that the sacrificial anode is there to protect the tank and that the galvanic corrosion of the tank increases as temperature rises, minerality of the fluid increases and the electric differential between the tank and ground increases (an electric water heater will corrode faster than a gas water heater, hence, I only use mine on propane). Anodes wear...that is their purpose and in water heaters, the "heating" process hastens that corrosion (that's why you don't find anodes in water accumulator tanks-no heating, particularly electrical and their tanks can be made electrically none conductive).
The "best" medicine would be to leave the tank full, electric heating element switch open with the battery disconnect "off", thereby minimizing the electrical differential applied to the dissimilar metals in the tanks. The reason your home tank "lasts so long" is that anode in your home tank is huge compared to the size of the anode contained in the pigmy water heater tank in your TT. If you could get a 50 gallon, or larger, water heater in your TT, the water tank would outlast the TT with no user maintenance at all...the sheer mass of a home water heater and its anode reduces the apparent galvanic reaction to a negligible point...much the same as an aircraft carrier sitting in the ocean (rust on those is also caused by galvanic action and those ships also have scrificial anodes attached to their hulls...)
There are also two schools of thought on the relief valve...one is that "exercising" it keeps the valve reliable, the other is that "exercising" it leads to leaking with a slight lessening of its reliability to release at the proper pressure load. I hold with the second school of thought. Everytime you open the valve, you compress the spring...constant spring compression weakens a spring (this is true of any spring - even the springs on your car and truck eventually "sag" from the constant compression and expansion). You also introduce a small amount of water to the sealing surfaces of the valve. As the water evaporates, it leaves minerals and these minerals accumulate, over time, decreasing the ability of the seal's surfaces to provide a leak free surface and they begin to "weep". The air in a hot water heater will naturally go to the highest point for escape and that point is the hot water outlet. There is nothing to be gained by "venting" or "purging" air from the tank using the pressure relief valve as it is at the same or slightly lower level than the hot water pipe to the plumbing system. I have never "purged" or "bled" any water heater tank using the pressure relief valve and as long as the seal is left intact (no water coating their surfaces) there is no corrosion between the seal (no dissimilar metals for galvanic action to occur) and no mineral coating to reduce the "seal", allowing the valve to leak or "weep" (I've never had a valve leak on any water heater or pressurized water system [my well pump also has a pressure relief valve]).
