I was taught that side effects are not so one-sided, and that changing output in response to outside state (such as the date) is also a side effect, a side effect on the function, rather than a side effect of the function, but I'm happy to use other definitions so long as they're commonly understood.
As I said before, though, even if JavaScript did throw an error as you'd prefer, it would still allow your function to have date-based problems. They'd be a bit noisier perhaps but no less present, and just as "well it's worked fine so far". And that's because, as I keep saying, the real problem here is using a function with inconsistent output and not thoroughly dealing with the possibilities. An API change wouldn't alter that. Most of the time it would still let you write bad code.
I also probably agree with you that errors are generally better than silence in response to bad input but, as someone else has said (more or less) it's not always unreasonable to consider "31st [Month]" as 31 days after the end of [Previous Month]. Without throwing errors, this flexibility is possible. Perhaps the creators believed having to mutate the day-of-month first was an acceptable trade-off for that.