Is the 4066 appropriate for power switching?
If you check the datasheet you'll see that the CD4066 has a rather high on-resistance. For instance, at 5V this is typical 470 ohm, maximum 1050 ohm (TI version). This is too much to switch any amount of current beyond something like 1 mA.
BTW, always design for worst case conditions, here the maximum value of 1050 ohm.