AVR: Timer overflow flag in TIFR
The point of writing 1 to clear is to clear the flag atomically without changing any of the other bits. Sure, it is possible to do a read-modify-write and clear one bit that way, but then you may overwrite a flag that got set in hardware between the read and the write. Since there is no reason to set the bit from software, the flip flop is configured so that the hardware can set the bit and the software can clear it by writing 1. This is not necessary for flags that are set in an interrupt handler as you can simply disable interrupts during the read-modify-write operation.

The other post does not mention anything anything about atomicity, which is the reasoning behind this design.