So are you saying if a device has a 0.5A @ 12V (6 Watts) wall wart, you can supply it with 1A @ 12V (12 Watts) without issues?
In almost every case, yes. The one time I've seen an exception to this had to do with the wimpy supply being part of the battery charging protection system, which IMHO is a huge cheat. They relied on the low current supply to limit how fast the battery would charge, instead of doing it in circuit.
Otherwise, for each device, when fed it's rated voltage, will consume no more current than specified, regardless of how much is available, and usually less than specified. This is true so long as there is no fault, which is what fuses are for. :)
Best,
Erik