Of all issues I have with this game, this is probably the least of them. Should I lose a match and claim that “it was because of the special support!”, this would definitely be an attempt at face-saving.
I presume that the poll was referring to event-specific special supports, BTW. I’ll address others in an addendum.
Now, there is one caveat, as well as an improvement that can be made.
The caveat: I’m assuming that the question was referring to correctly working special supports, not things like “Zhalfirin Void support does nothing”, “Great Tournament support not changing colour”, “Orzhov RT support has Izzet effect”, and similar, which are bugs and should really be discussed in that channel.
The improvement: Colour change in these supports would be greatly improved if it worked according to a set rotation (eg, W,U,B,G,R,W…) or the gem retains it’s colour and does not change. A randomised system has the risk of exacerbating excessive cascading, especially if the randomisation is imperfect on a gross scale. The rule of colour change should be listed along with the other rules of the event.
As for where they should go, my answer is “where they make sense”. Something like Dragon War (where they can be seen as the “help” given by that Elder Dragon in whose node you’re playing) is perfectly appropriate. As for PvE, I’d rather face the Void or Azor with their special privileges than Bolas and his HP bunker - they require more intelligence and less looping and brute force to get around.
Putting some such supports into ZvE would just be so much garnish.
ADDENDUM: SPECIAL SUPPORTS CREATED BY PLANESWALKERS
Many PWs make supports as a 3rd ability. The standard ones are around shield 6 (Liliana 3’s shield 4 one and Koth’s shield 10 one are the maxima and minima of the distribution, to my knowledge).
Then there are the 2 that make indestructible supports: Bolas and his Spark and Kaya 2.
The Spark makes that particular Bolas too strong in comparison to the other Bolas iterations, not to mention other planeswalkers.
Kaya was better designed, in that she was not given the equivalent of a superpower.
These supports behave like the other special supports despite appearing semi-randomly, so they warrant a mention for the sake of completeness.
Discussion around them is more about planeswalker balance, which is off-topic here.
CORRECTION
I stated that Kaya makes an infinite shield support. She does not.
The planeswalker I had in mind was Vraska 2. Apologies for talking rubbish.
I am leaving the piece as written for the sake of completeness.