To test the RPi GPIO delays I used this short code

#include <pigpio.h>

int main(void)
{
    gpioInitialise();
    gpioSetMode(2, PI_OUTPUT);

    for (int i = 0; i < 10000000; i++)
    {
        gpioWrite(2, 1);
        gpioWrite(2, 0);
    }

    return 0;
} 

The compiled program ran on Pi Zero with no other programs on the background. Output was captured with the logic analyzer and it doesn't look so good

I ran the parser on the captured output writing precise timings to a file, this snipper shows average output

time:    0.125000 µs, state: 0
time:    1.000000 µs, state: 1
time:    0.125000 µs, state: 0
time:    0.250000 µs, state: 1
time:    0.125000 µs, state: 0
time:    0.250000 µs, state: 1
time:    0.125000 µs, state: 0
time:    0.250000 µs, state: 1
time:    0.125000 µs, state: 0
time:    0.125000 µs, state: 1
time:    0.250000 µs, state: 0
time:    0.125000 µs, state: 1
time:    0.250000 µs, state: 0
time:    0.125000 µs, state: 1
time:    0.250000 µs, state: 0
time:    0.125000 µs, state: 1
time:    0.250000 µs, state: 0
time:    0.125000 µs, state: 1
time:    0.250000 µs, state: 0
time:    0.125000 µs, state: 1
time:    0.250000 µs, state: 0
time:    0.125000 µs, state: 1
time:    0.250000 µs, state: 0

This doesn't look so bad. But when sorting the output you'll start to notice that the output is not stable. At most the delay is about 4300 times more than expected.

$ cat capture.txt | awk '{if ($2 > 100) {print $2}}' | sort -n
101.000000                                                                     
104.125000
105.875000
107.125000
108.375000
109.250000
109.500000
110.500000
110.875000
112.750000
114.625000
114.750000
115.250000
115.625000
117.750000
120.250000
121.500000
122.000000
122.750000
123.500000
133.375000
142.125000
146.875000
148.625000
149.250000
149.375000
149.875000
194.250000
200.625000
207.625000
230.625000
236.125000
236.500000
269.875000
351.750000
445.500000
451.500000
538.625000

And this is on an idle Pi Zero (load avg 0.09), imagine the delays on a Pi with more load. It could work sometimes, but I need to trust that the remote works without failures more than 99% of time. Looks like the remote needs a separate microcontroller.