Sure, you should not shut down ideas when brainstorming solutions, but there's a point between brainstorming and implementation where the ideas do need to be reviewed mercilessly. The problem in the parent poster's company wasn't that they brainstormed about a home-made project tracker, it was that they went through with spending development effort on that.

The brainstorming process is designed for generating alternatives, it's not suitable for choosing between alternatives, that needs to be done in a critical "anti-brainstorming" mindset.