The 5V tolerant means you can use pull-ups in the open drain configuration, and doesn't work with push pull. This means you could possibly use a pull up to 5V and open drain, keep in mind that this method can be slower if you have too much capacitance on the digital line, the RC time constant will need to be calculated.
This means if you remove the buffer, you'll need a pull up and the speeds will probably be reduced more than your design needs.
In my designs with the STM32F4, I usually stick with a buffer and push pull for fast speeds. If the design also calls for level translation, I'd stick with the TXS0108E.
If your using the GPIO's STM32F4 as inputs, then I would consider how much current the input can be sourced. It must not exceed 5mA.
The datasheet explicitly states that the power must not exceed Vdd+4V. If the peripheral is at 5V and the Vdd is at 0V, then technically you would be violating the absolute maximum ratings. The question is: why? The protection diode turns on, heats up and burns out, potentially putting the input transistors at risk.
This is where I personally might thumb my nose at the datasheet. I don't know if I would recommend other people doing this, but if I were doing this myself, I would be comfortable limiting the current sufficiently with series limiting resistors on the inputs to prevent excess current from reaching the diode. The datasheet also states that no more than 5mA into the input port max. So if the peripheral speed could support a 200Ω series limiting resistor then you might be able to ditch the TXS0108E for a series limiting resistor of more than 200Ω.
Another thing to think about, if the supplies only take a short time, maybe under 1ms to come up. Then the time that the input protection diode would experience any current would be short, and it would also be fine.