Why were true-breeding pea plants important for Mendel's experiments?

Because their genetic make up is known for sure to be homozygous so the offspring's genotype is known for sure. This means that the phenotype of the offspring can tell which trait is dominant.

If we have two parents which are true breed for one trait, for example red color versus white color in flowers. One parent is true breed red and the other is true breed white. The offspring will be for sure heterozygous as it gets one allele from each parent. If the offspring is red in color, then the red is a dominant feature, and if the offspring is pink, then the two traits are codominant.