When is SPI.beginTransaction required?
It appears calling the method beginTransaction() prevents additional SPI transactions from interrupting the current transaction.  Calling endTransaction() allows access to the SPI hardware again. This added complexity may sound odd.  Especially in the simple Arduino sketch-writing paradigm.  But as programs grow in complexity, more SPI devices are added and interrupts are used to quickly access SPI devices - the likely hood of SPI contention increases.
In the SPIClass source code, there is this comment immediately before the beginTransaction() method:
  // Before using SPI.transfer() or asserting chip select pins,
  // this function is used to gain exclusive access to the SPI bus
  // and configure the correct settings.

So, it may be, that if the sketch-code is particularly well behaved and does not need protection from accidentally using the SPI hardware from multiple concurrent transactions, that these two methods need not be used.  But why take the chance.