Can't set ffmpeg request header when using file for input
When a single input is directed fed to ffmpeg (-i), various options can be set on it, depending on what the input reader allows and recognizes.

However, FFmpeg does not natively read an input list from a text file. There's a bespoke module called the concat demuxer, invoked by -f concat, which parses the input list, opens each file and concatenates them. To the main ffmpeg pipeline, this is presented as a single input, generated by the concat module. And the concat module does not recognize or carry over options meant for the individual files listed within the text file. All listed files can only be opened with default parameters of their respective demuxers/decoders/protocols..etc. This is a limitation. You may open a feature request at trac.ffmpeg.org to change this.

What you could do is read all inputs directly.

ffmpeg \
    -headers $'Content-Type: audio/wav\r\n' \
    -i 'https://google1.com' \
    -headers $'Content-Type: audio/wav\r\n' \
    -i 'https://google2.com' \
    -headers $'Content-Type: audio/wav\r\n' \
    -i 'https://google3.com' \
    -headers $'Content-Type: audio/wav\r\n' \
    -i 'https://google4.com' \
    -filter_complex "[0][1][2][3]concat=n=4:v=0:a=1" \
    'output.wav'


For WAV inputs, re-encoding to WAV won't lose quality.