Bodmer does support 800x480 via 8080-8 Parallel interface. However I have never used his particular driver.
Actually native SPI can work pretty fast with the correct library and target. e.g. ST7796S with TFT_eSPI on an ESP32. SPI can use DMA. Parallel can't really use DMA.
When Arduino was born there were only AVR targets. Careful use of Parallel was much faster than the AVR's crap SPI peripheral.
Nowadays there are SAM3X, SAMD21, STM32, ESP8266, ESP32, Teensy, ... targets.
Most of the Arduino SPI class implementations on these other targets are really, really, really crap. (except ESP32, Teensy)
Individual TFT libraries might handle the SPI themselves e.g. Bodmer makes STM32 work well.
Adafruit optimise for their brand of target MCU. While leaving the non-Adafruit official Arduino SAMD21 targets with poor performance.
It does become very fiddly if you try to support multiple targets, architectures etc.
There is always room for improvement. Explain your "problem".