Why might Louis XVI have had such difficulty dealing with France's myriad problems when he became king?

It would be because the state the country befalls before his rule. The monarchy's expenses is very expensive and the country's state of the lower-class is deteriorating exponentially. Also the discontent and the rise of new thinkers brought new ideas of change and equality that solidifies the cries of revolutions.

Anyone would have had difficulty dealing with the myriad problems of France's kingdom if they came into the kingship at the time Louis XVI did. Louis XIV had established a system which created success for his own reign but established a top-heavy state that would be impossible to maintai, and Louis XV had not managed the kingdom's finances or politics well.

Louis XVI personally did not have the personality or aptitude to serve as a strong king. He would much rather go hunting or work on the mechanics of a clock than deal with the necessities of running a kingdom. He was the wrong man coming to the throne at the wrong time. Revolution was becoming more and more inevitable in France.