This is very much a corner case. Usually
X spells or abilities do state that
X cannot be zero. However we are looking at cards that have other text restricting
X. All of them are from old sets. At the time of their printing, it did not matter if
X could be zero. It is only with interactions with cards printed many years later that it matters.
There are only 7 cards that specify that only a specific color of mana may be used for
X.
Three have the
X in their mana cost. Mana costs (printed in the upper right corner) always permit
X to be cast for 0 because there are many effects that let you cast spells without paying their mana cost. -
Consume Spirit,
Drain Life,
Soul BurnAnother three are creatures with activated abilities that have such text. -
Atalya, Samite Master;
Crimson Hellkite;
Crypt RatsAnd the seventh is
Emblazoned Golem with this text tied to the kicker ability. Kicker is not an activated ability. It is a static ability that lets you pay an additional cost when casting the spell.
To be honest ... after much research and pouring through the Comprehensive Rules ... I am stumped.
I am 100% certain that
Drain Life and the like can be cast for an
X of zero. This is because there many effects in Magic that permit you to cast spells without paying their mana costs, and so this contingency is accounted for in the rules.
For
Crimson Hellkite, I am 50/50 on it. Mana costs (in the upper right hand of the card) and activation costs are treated differently by the rules. They do not let you pay resources that you do not have. Since zero mana can't be red, you can't pay zero red mana. But I can see the argument both ways. Here's where I'm really stumped.
Because of this, I'm only 75% certain that you can't announce kicking
Emblazoned Golem for zero. My gut still says that because it is an additional cost, you can only
opt into it if you can actually pay it. Zero mana can't be of a specific color, so it cannot be paid.
If you have access to some judges, I would ask a few. Because this is such a corner case involving such an old card (and truly only ONE card), I would seek multiple opinions from judges.