I wouldn't call it a power loss; that suggests not having enough power. It would be a power waste in that the differential between input an output of a regulator is burned off as heat. e.g. for the 7812 the input is 19, the output 12 so 7 volts is 'burned off'. How much power is wasted can be determined by multiplying the voltage differential by the current going through the device. If your not energizing the solenoid ALOT, I wouldn't worry about it unless your running off a battery or battery pack; and I doubt that since 19 v would be an uncommon battery voltage. Same with the 7805. With your circuit you are only powering two ICs and the logic voltage they use is only for signals. The other way to go about it is to use switching regulators but they are significantly costlier.
Using a voltage divider for power is pretty much a no-no. In order not to have significant current flowing through the divider when connected across a potential, you've got to use some pretty high resistances. When you go to power a device with the divider, one or the other of those resistances will be in series with that load. A good amount of the voltage you need for your device will be dropped across the resistor.
Keep in mind that the 78xx series of regulators are only good for about an amp. They both have big brothers available in a TO3 package good for about 3 amps.
- Scotty