It could be that Rasberry Pi 1 is not powerful enough for the Pulse Audio backend.
Therefore revert to an earlier version of Librespot that also provides the ALSA backend on Rasperry Pi 1.
Current Librespot for LibreELEC releases exclusively play via Kodi, because this works out of the box without interfering with Kodi audio. Unfortunately, this requires more computer resources.
Thanks a lot for the info! Maybe instead of running an earlier version of Librespot it's time to upgrade the hardware, even though I don't like to discard things that are not broken...