MTG: An Emblem that would remove itself
One issue with the wording is that &quot;remove from game&quot; is text that MTG used to use prior to the 2010 rules update, and all cards that said to remove something from the game were given errata to say that they exile it instead.
Because of this, &quot;remove this emblem from the game&quot; could easily be confused with &quot;exile this emblem&quot;, as people have learned that things that say &quot;remove from the game&quot; actually now say &quot;exile&quot;.
There is no wording on any existing abilities or effects that actually remove something from the game (AWOL excluded). Things are only removed from the game through rules that use the wording &quot;ceases to exist&quot;, such as a token not on the battlefield; or &quot;leaves the game&quot;, such as objects owned by a player leaves the game. Neither of these translate well into an effect that could be written on an ability.
That being said, I don't see any issue with the emblem saying &quot;Exile this: Add one mana of any color or one colorless mana&quot;. Sure it's a bit weird to have an emblem hanging around in the exile zone; but it will have no effect on the game. Its ability cannot do anything while in exile:

114.4. Abilities of emblems function in the command zone.

And there wouldn't be any way to ever remove it from exile; anything in the game that gets things back from exile specifies what type of thing it can bring back.
But if you were modifying rules anyway, you could always go ahead and alter 704.5 to make it so that the emblem doesn't hang around:

704.5d If a token is in a zone other than the battlefield, it ceases to exist.
704.5e If a copy of a spell is in a zone other than the stack, it ceases to exist. If a copy of a card is in any zone other than the stack or the battlefield, it ceases to exist.

Append a new state-based action similar to those two:

704.5f If an emblem is in any zone other than the command zone, it ceases to exist.


In terms of your second idea of making it a one-per-game activated ability that costs {0}, I don't see any issues related to possible cost-increasers, because 99% of the time, the right move is going to be to use that ability on turn 1, maybe turn 2; making it very unlikely your opponent will have gotten an increaser out. And also cards like Suppression Field do not work on mana abilities, which this is.