"I don't see a problem with putting C1 on the input side of the switch. If the switch is located close to the XLR and the chassis wire from pin 1 to C1 is above average thickness, that would certainly work fine and it is true that it would eliminate those currents through the switch contacts.
But I would keep R1 in front of C1. You could have an unpowered device like a dynamic mic (and phantom was on just by accident) that doesn't have large caps on the lines so that RC is potentially good filtering. And now you have potentially a bunch of C1's in parallel so you need them to limit surge currents on startup."
I agree with the above statements particularly with regard to inrush limiting current into the C1s on rail power up. In most consumer equipment those would also be fusible resistors in case C1 shorted.
I checked the current specs for some of the smaller latching pushbuttons.
Illuminated Push Button Switches | LED Push Button Switches
Many of the smaller latching switches we see in common use for phantom in commercial products are only rated at 30V 100 mA.
The 3 dB point of 200 Ohm 220 uF is 3.6 Hz. The filtering provided however is common mode so most LF noise would be rejected anyway without it. One could argue for a smaller C1 for less stored charge and supply rail power-up inrush.
I think the worst case condition WRT ramping would be a dynamic mic feeding a transformer input. When phantom is (accidentally) switched on both legs rise instantly and do so in common mode. No magnetizing current would develop in the primary and the CMRR of the transformer would largely reject the pop. The DCR of the mic would also shunt the primary.
When not under fault conditions the 6K81s are always going to limit current from the 48V supply. Faults and currents from stored charges - as emrr points out - are another matter.
In an active mic preamp with an open input there is a common mode step response during phantom turn on on the "dry" right-hand side of the input capacitors. At t=0 the input coupling capacitors are a dead short. A voltage divider is formed by the phantom pull-ups and the input bias resistors. For a 1K bias resistor there's about a +6V common mode step at the preamp inputs. A good preamp's CMRR will reject this step. But, and its a big but, there will always be common mode to differential conversion because the time constants of the input capacitors don't exactly match nor do the resistors. For this reason it's always a good idea to keep the bias resistors low enough that the step at turn-on doesn't exceed the common mode range of the preamp.
The point is no matter how much you slug the phantom turn on it's going to pop. And, in most cases that are capacitively-coupled the time constants of the phantom pullup resistors are going to dominate turn-on time.
Phantom on LEDs should be bicolor red/green for danger/safe indication.