This way of rooting is called mid-point rooting. Vary the parameters used by the different programs, such as the seed value and jumble factor for the order of OTU addition. When in doubt, apply various evolutionary models for matrix construction. Add or remove one or more OTUs and see how this influences tree topology. Try to include an outgroup that may serve as a root for your tree.
Some information is said to be lost.
However, this is usually a small fraction of the data. Maximum parsimony uses only the relevant sites. Maximum parsimony is notorious for its sensitivity to codon bias and unequal rates of evolution. None of the methods is reliable when OTUs with highly unequal evolutionary separation are included in the data set. . The presence of more than one homologue of a certain gene, or of different members of a gene family, in one and the same organism may complicate considerably phylogenetic analyses.