It's in the "bible" - compatibility reasons. 8051 was meant to be "mostly compatible" with 8048. Why it has a 13-bit timer - well, that's a question...

It is not uncertain, the timer still runs. It is essentially the same as using the 13-bit mode, with the difference that TL0 counts up to 256 rather than up to 32. You can do the same trick with reloading THx only, with a difference that it needs to be reloaded within 256 cycles rather than 32 (and your timing has a Xtal/12/256 granularity, rather than Xtal/12/32; and the interrupt can run 8x slower).
And you can still compensate for interrupt latency by subtracting the current timer value from the reload value - so you get a non-multiple-of-32(256) 16-bit divider for your timing ticks (but the interrupt service routine gets a bit more complicated). For example see Peter Dannegger's page (I referenced to it in the other thread on the same topic today).

Jan Waclawek