I haven’t lifted any statues to check honestly, but I would say it isn’t a usual thing to do.
Statues that are for dead children are often dressed in knitted clothing to keep them “warm”. You can see them congregated around shrines everywhere in the country, but Jizo are also placed in forests and along paths as they are protectors of people that are travelling.
Here is what Jizo for dead children look like oftentimes:
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A Jizo being on the Sengawa river walk wouldn’t be out of place even if the murders hadn’t happened. But it’s the fact this one appeared so soon after, was placed close, and had the number carved in the bottom. That’s a bit suspicious, but as we’ve been discussing here it could also be not suspicious at all.
As for shrines and temples they are all over the place, especially in Tokyo. You’re never really far from one in most places.