One place where polled Tx makes sense is with smarter UARTs with hardware fifos, like those on ARM controllers. There's less overhead by loading up a fifo (polling fifo full flag) and waiting for a single tx interrupt when the fifo empties. I don't know of any 8051s that use fifos.

Another use of polled tx, especially if the data rate is low, is to ensure there is a gap between characters. When the baud rate generator isn't exact, say 1-2 percent error on clock rate (or same on receiver end) then sending long strings of data at the fastest possible rate may result in a missed bit. A small gap between bytes generated by the nature of asynchronous polling instead of synchronous interrupts allows time for the remote receiver to realign the bit sampling window. I do this with some SiLabs 8051 controllers to compensate for the 2% variance in the internal oscillator, though I use a timer to generate a gap instead of polling TI.