Self Elimination Game - Good Idea or Not?

What if I end up with 2 pieces due to matching more than 3 at a time?

The game has a weird quirk that you can't block your opponent effectively once you start winning, due to lack of pieces. I have a sense that strategy would start to disappear as the game progressed.

I think the game as described could easily get bogged down into a tic-tac-toe kind of tie with everyone blocking each other's moves. Mechanisms to prevent that might present themselves while noodling around with a prototype.

For example, maybe you can only place within a certain radius of your existing pieces. The player who goes first might be content to play separately, but the second player has an incentive to reach across the board and cause some problems.

Stacking might be a good way to liberate blocked/trapped pieces. Maybe every piece beyond the third that's eliminated at once can be stacked onto existing pieces. A stack-of-two can be removed with any adjacent friendly piece because they add up to three. A completely surrounded piece can even get rescued by making a stack of three. The ultimate move would then be to arrange a diamond of four stacks-of-two, then place one piece in the middle to eliminate 9 simultaneously... those six could be stacked elsewhere leading to a chain reaction that could conceivably remove every piece in play. (Note, if your opponent doesn't put their own piece in that center spot, you're obviously playing a 4-year-old).

As OK Play illustrates, the board is not essential to this kind of game... unless you make it essential.

One idea is to do something similar to Scrabble... litter the board with buffs or obstacles.

I think a better idea would be to have two versions of the game. The basic version would be as you described (with any fixes we don't know about yet), and the advanced version where pieces can "wrap-around" connect with the opposite side of the board.

Even if you don't want to do that, completely artificial barriers like a board edge can make for deeper strategy. Note how much less useful a chess knight is on the left or right edge, or how the basketball rule of "once you stop dribbling you can't start again" forces a lot of passing and therefore opportunities for the defense to intercept.