STM32 SPI w/ DMA "BUSY" flag set
What exactly is throttling the SPI transfers? If you're using DMA directly (rather than triggered by a timer or something else), then as soon as the SPI is free, the DMA peripheral would start another transfer. As a result, being busy all the time would be expected.
According to the manual for the STM32F1xx series, section 25.3.7 (other series should have similar behavior):

When communication is not continuous, the BSY flag is low between each communication.
When communication is continuous:
● in master mode, the BSY flag is kept high during all the transfers