The switch makes sense, then, you'd need some fancy programming to use only one in that case.
The servos definitely are the current hogs here, that's why if you're going to have extra decoupling caps, it's good to have them near there. The neopixels are designed to be placed individually in long strings, so while I don't know if they have internal decoupling, they are probably designed to be able to operate in noisy environments.
There will definitely be noise on the power rail because of the servos, but I doubt it will be problematic with 2000uF of decoupling and the on-board decoupling for the micro so long as the switchmode converter can actually deliver it. I wouldn't be surprised if removing the 0.1uF caps, the 470 ohm resistors, the BAT54S diodes, and the zener (?) diode from the schematic entirely would work the same as as proposed in the vast majority of situations.
As a matter of flexibility, I'd move the 10k resistor divider from pin 1 to pin 21, so you can use it as an analog input to monitor the 9V in addition to just a digital reading... and if you don't need to monitor it or check it, just removing them too is an option - not exactly sure what requirement it fills.
Regardless of what schematic you settle on, it could be worth trying some elements of the other to see how they actually effect things - the parts required are pretty cheap, so it's basically only the time investment in the rework (which is almost nothing if you use a solderless breadboard to test it first!)
For the post that's appeared before I could post this reply:
Fair enough with the 470s, then, I hadn't heard of such requirements for neopixels and have never implemented series resistors on the PWM control pins for interfacing with a micro, myself, but if there are instances where it's useful, they're certainly not a big ask, and I doubt either will have any negative effects.