KDE System Settings don't remember connector for built-in audio

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Turns out the problem was that PulseAudio didn't pick the right port for the given sink. User "hello"'s suggestion got me on the right track. In my case, the built-in card has index 1 and lists, among others:

index: 1
    name: <alsa_card.pci-0000_00_1b.0>
    driver: <module-alsa-card.c>
    owner module: 7
    properties:
            alsa.card = "1"
            alsa.card_name = "HDA Intel"
            alsa.long_card_name = "HDA Intel at 0xfe8f4000 irq 45"
            alsa.driver_name = "snd_hda_intel"
            device.description = "Built-in Audio"
            #....
    profiles:
            input:analog-stereo: Analog Stereo Input (priority 60, available: unknown)
            output:analog-stereo: Analog Stereo Output (priority 6000, available: unknown)
            #....
    active profile: <output:analog-stereo+input:analog-stereo>
    sinks:
            alsa_output.pci-0000_00_1b.0.analog-stereo/#0: Built-in Audio Analog Stereo
    sources:
            alsa_output.pci-0000_00_1b.0.analog-stereo.monitor/#1: Monitor of Built-in Audio Analog Stereo
            alsa_input.pci-0000_00_1b.0.analog-stereo/#2: Built-in Audio Analog Stereo
    ports:
            # ...
            analog-output-lineout: Line Out (priority 9900, latency offset 0 usec, available: no)
                    properties:

            analog-output-headphones: Headphones (priority 9000, latency offset 0 usec, available: no)
                    properties:
                            device.icon_name = "audio-headphones"

So it's pretty obvious that the idea is to se the default port for the (only) sound sink. I did this by adding the following to /etc/pulse/default.pa:

set-sink-port alsa_output.pci-0000_00_1b.0.analog-stereo analog-output-lineout

I did not need to wipe any existing state in my home directory.