We cannot give correct explanation why deoxyribonucleic acid (DNA) elements have not been successful in the yeast genome.
Yeast has a compact genome with 70% of its DNA representing exons. Hence, it may not have sufficient "safe havens" for DNA transposition.
Transposons or transposition events, which kill the host organism, cannot spread. The Ty elements of yeast have evolved mechanisms that target their insertions, so that it may not harm their host.
It may be just a chance that yeast does not have DNA transposons. Yeast also has specific mechanism to prevent their spread.
We can still look for the related species of yeast to determine whether they have class 2 elements.