'Why didn't' questions can be difficult to answer, because then you're trying to prove a negative. Regardless, the situation was never as clear cut as 'Byzantine Empire okay, Turkic beyliks weak and divided'. The Byzantine Empire was itself facing numerous challenges during the 1300s. Serbia grew very powerful at the expense of Byzantine territory in the west. Bulgaria remained a threat to the north. The Byzantine Empire went through a civil war. It was ravaged by the bubonic plague. It suffered from earthquakes. It had religious troubles. And around halfway through the century, the Ottomans had become so large and powerful that the window of opportunity you described had largely passed. From then on the Ottomans went on the offensive and the Byzantines had to defend.