Doug's Musical Ability, in GURPS

[Shepherd]

Yes, but it’s not memorizing the forms that Doug’s doing, he’s keeping the triggers handy.  Each song triggers a specific change, not Doug pulling out a memorized form. 
ETA: Memorizing Forms is only relevant if you're capable of changing automatically.  Doug can't.  He has to have his trigger, so he doesn't memorize any forms.  He can't, willingly, change forms without his songs, so he doesn't need to be able to memorize any forms.

The problem is that the Cannot Memorize Forms limitation is designed around a Morph that requires you to see or touch a living being in order to change into it. If Photocopier-Guy wants Superman's powers, he must interact with Superman (and not just a picture of him). If he then wants Martian Manhunter's powers, he must interact with Martian Manhunter. If he then decides that he liked having Superman's powers more, he has to go back and interact with Superman again. This is why it is a -50% limitation. Without that limitation, Photocopier-Guy (who has an IQ of 14) could manifest the powers of Superman, Martian Manhunter, and a dozen of their Justice League buddies at will.
Doug's powers are significantly more awesome than those of Photocopier-Guy, as Doug knows hundreds of power templates. Doug is not operating under a limitation, much less a -50% limitation; his power has (at least) one major enhancement. Since the Cosmic enhancement lets you break the rules in specific ways, a +50% to the power cost could give Doug an unlimited number of possible forms in his power catalog. Since listening to songs (which can be accomplished with an iPod) is much easier that seeing/touching specific beings, that would probably count as a seperate +20% enhancement.

I’m okay with that. That removes the need for “Always On” with a mitigator, though we still need something (probably a Nuisance Effect) to prevent the change when other music is playing.

That would be an Accessibility limitation.

This, I disagree with. Doug doesn’t need to make an Ultra Power check. Using Morph totally negates the need for it. And DW shows that he really doesn’t have to do anything special other than listen to music . . . and not be stupid about it.

While he may not need a power check to use a song, Doug almost certainly has Ultra Power anyway. It easily explains the times he pushes a particular song past its regular limits (ie. his use of White Wedding during the Bubblegum Crisis step). Ultra Power is also useful for acts of superheroics that don't involve his music powers. Since he has the advantage anyway, it also makes a good mechanism for forcing a new power song to manifest during combat.

The points for the “template” do not get reduced. They’re paid for fully. It’s the Morph Advantage that gets the reduction.

You misunderstood me. I wasn't talking about applying a cost reduction to the Morph "template". I was comparing the cost of Morph + Template to the cost of Modular Abilities (cosmic power). Since that advantage is worth ten points per level and the biggest discount you can get on an advantage is -80%, the minimum cost of Modular Abilities (cosmic power) winds up as twice the cost of Doug's most expensive template. Unless the cost of Morph winds up higher than Doug's most expensive template (highly unlikely), Morph is the cheaper way to go.
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"Anyone can be a winner if their definition of victory is flexible enough." - The DM of the Rings XXXV