It may be due to inhibiting/preventing permanent phosphorylation of certain markers or regulators of polarity. As a polarized cell would mean that the stem cell would be differentiated, and to maintain polarity, certain complexes within the cell must be phosphorylated. With high levels of alkaline phosphetase, polarity regulators, even if they do become phophorylated (wont stay phosphorylated for long) with high levels of alkaline phosphetase (which works to remove phosphate from molecules) no polarity complexes will stay phosphorylated, therefore no polarity, therefore more mesnchymal and undifferentiated and more like a stem cell, a stem cell can be. Although this all seems to make sense- dont forget that if alkaline phosphetase was to be too high,(so perhaps there is a critical level, whereby alkaline phosphetase levels actually work to in favout of differentiating the cell!) The STAT3 pathway needs phosphorylation to drive self renewal and pleuripotency- so there must be a balance there somewhere. This is just an educated guess- I am a 2nd year biomed student. Hope this gives you some clarification!