Pure-tone sirens are necessarily noisy; a while back there was an attempt to replace them with alternating white noise and a more normal siren sound, the reasoning being that sirens only needed to be so loud because they were serving two different goals at the same time, to identify the existence and location of an emergency vehicle, and that white noise could be played at a much lower volume while making it easier to locate the vehicle relative to your own.

Also anecdotally: I live on a busy cross-roads in Berlin, and I've had half a dozen so far today… and one more while writing this line. The exact number varies a lot from one day to the next, so I'm not sure the overall count, but the new one is still going on by the time I get to this word ← here even though the road was fairly clear at the moment.

Sometimes I even get them in stereo as multiple vehicles go past with a gap between them; and I've witnessed at least one occasion where different services passed the junction in different directions within a few seconds of each other.

The sirens are the only bit about this place that I really dislike; but enough of a problem that I'm looking for a suburban place next even though that will probably mean a longer walk to shops and restaurants.

Of course they are necessary. They have to be used responsibly and not as a job perk, that's my point. Light signals are usually enough.

I also live in 1.5 mil city and I haven't got used to how many there are after moving here almost a decade ago.

Same in NL. Sirens are only turned on in the most extreme cases. In most cases lights seem to be enough. I do get the impression that firefighters are a bit more likely to use sirens than police and ambulance are, but I'm fine with that.

Except in London, where hearing a siren is so common people (other than drivers) don't react.