Not an EE but I would venture to say that board real estate would become a major factor. How many discrete transistors can you place in the area occupied by a single SMD '244? if you use 1 transistor for each signal you do not have driven rail to rail output. The 244 you referenced has eight channels of +/- 24 mA at 0 & +5 Volts and a propagation delay of no more than 7.5 ns.
I'm sure someone could cobble together a discrete buffer but with the circuit complexities of a discrete rail to rail buffer is it really worth the effort?