TCA9548A Reset Pullup Resistor
The datasheet actually says, in section 8.4.2:


  The RESET input must be connected to VCC through a pull-up resistor


Please note the level of assertion: MUST. It is therefore the condition when manufacturer guaranteed the IC to function correctly.

According to the datasheet, Table 6.5 DC characteristics, the RESETn pin is listed a having leakage anywhere from +1 uA to -1 uA. If you leave  this pin unconnected, it might assume some middle level in vicinity of switching threshold, and can begin to oscillate like hell, screwing all things. The effect might be spurious, depend on ambient humidity and temperature, affecting maybe 20-30% of your boards.

If you decide to connect this pin to VCC directly, you might run into another trouble. Again, according to the datasheet, it takes only 6 ns for the RESET to go active and reset all internal circuits. Only 6 ns !!!. You might be even unable to see this glitch even with a good oscilloscope. It is well known that power rails can have glitches due to logic switching around, and bypass caps can't be placed at every centimeter of board. So glitches on power rails do happen, and they might reset your mux configuration in the middle of operations. But if you use say, a 10k pullup, together with 5 pF input pin capacitance you will have a 50-ns filter at least.

But instead of listening to all this musing about glitches, leakages etc. you could simply follow manufacturer's requirement and get a working device without wasting your time. Always assume that there is a reason behind every manufacturer's requirement.