It's not entirely true that you can't use an AC-DC power supply to power your laser. However, unless you're buying an audio-quality power supply, which is already regulated for filtering out noise and spikes, you need to have a regulator circuit in between, like a traditional LM317 regulator circuit (aka a
DDL circuit). Another problem is that most AC-DC transformers don't provide sufficient current for powering higher-current lasers. I wasn't able to use mine for testing a 445nm on its dummy load, so I had to attach it up to the batteries which was a pain.
If you'd like to power your laser from the wall, buy a
9VDC wall-power supply, and a
DC Barrel Jack. Then you need to connect the barrel jack to a regulator circuit such as a DDL circuit for actually connecting to your laser. I've also used
this breadboard power supply for simply providing 5V regulated voltage for various projects, including lasers. It has nice clean power, and can be modded into a DDL circuit as well with some modifications (I haven't actually performed the mod yet).
Never use two voltage sources in parallel unless they're matched (i.e. have exactly the same voltage characteristics). Usually only specially selected batteries from the same production batch can be connected in parallel to provide higher current and capacity. The reason not to? There will be a voltage difference between the two batteries and the batteries will "fight" each other as they try to equalize the charge between them. This can damage the batteries and possibly cause a lot of heat from the rapid flow of charge between the two batteries.