My first guess, without doing any research, is that such lights would be in violation of the Anaheim Resort District's zoning and use laws.
Not True At All, in fact the resort district has more freedom than any other area in Anaheim. Its the entertainment region, Baseball Games (Angel Stadium), Hockey Games, Concerts (Honda Center), and Disneyland with all its Fireworks and glory happen here every night.
Hollywood land always has had search Lights since they began Dance Parties in Hollywood land, they have about Six! All in a Circle at Mad T Party, they used the same Search Lights for elecTRONica.
There on every night when Mad T Party Is happening from 6 or 7 - Close.
Also in Disneyland itself, there is a spotlight from Space Mountain, and when ever there is a dance party in Disneyland.
You can even see DCA's spotlights from Disney is you look. Attracting the guest to the Mad Tea Party in Hollywoodland. I agree they would look great on the Hyperion facade, but the facade is pretty crappy so it might be underwhelming.
I feel like spotlights would look great on the Carthay, especially since they want more guest to come in. Why not make the area recreate the opening day of Snow White each day, it'll make it more lively.
For what it's worth, having fullscale searchlights out every day as part of park deco would radically diminish the impact they have when Disney's using them to draw attention to the limited duration dance parties etc. - using them as punctuation keeps them as an attention focus, not "oh, that's just the Hyperion".
Credibility is to be sought for. Credulity is not. Sadly the latter is our normal human state.