I'd still have complained.
The issue isn't that the story wasn't newsworthy and merited some coverage but that the BBC, by streaming the same feed simultaneously on multiple channels, didn't provide an alternative for license fee payers, and especially those who don't subscribe to cable TV or Netflix/Prime Video. That there are these alternatives is irrelevant to the decision taken by BBC management to indulge in an OTT exercise in sycophantic virtue signalling, no doubt in case they were ever criticised for not being sufficiently sycophantic (as was, iirc, the case when the Queen's mother died a dew years ago).
It's not just the BBC that are being sycophantic though - the moving of sporting events on Saturday, so that nobody is professionally kicking a ball or riding a racehorse while a certain family funeral is taking place, is also an overreaction
There is also another really worrying aspect.
No got much publicity, but all campaigning for the various elections at the beginning of May has been suspended until after the funeral. So 8 days of campaigning has been lost. And campaigns are important within our democratic process to set out manifestos and have them challenged. To lose over a week of campaigning is a real challenge to the democratic process and while many of the elections aren't particularly critical, the one in Scotland could be key in determining whether the UK as we know it exists in a few years time.