My guess is it’s also a matter of practical usage: they’re made of heavy iron and a round one will fall in place whatever orientation it’s thrown over the cover, while a different shape needs to be carefully oriented. I suspect this also means less broken fingers.

But round one is easier to steal.. just roll them off. Whereas a square or any such shape, would be very inconvenient to move.

[Edit in response to a question]

Some people have attempted to steal manhole covers in order to sell them for scrap metal. China Daily notes that there has also been a problem with taxi drivers removing manhole covers to "steal water and clean their vehicles". https://www.bbc.com/news/blogs-news-from-elsewhere-52400235

If you're going around stealing covers, you're probably driving a truck and carrying them in the truck bed.

Who steals iron to turn in for scrap? It's only worth about 10 cents a lb. And then you have to haul it to the scrap yard. It's heavy!

On the other hand, copper is $3/lb, brass $2/lb, aluminum is $0.50/lb

Read "Playing the Moldovans at Tennis". According to that book, most of the manhole covers had been stolen for scrap.

Why would someone steal a manhole cover?

If Google is asking about them on an interview they must be important.

It's a very common thing to steal. Lots of iron. That's why they use concrete-filled ones. That's why they are stamped so a scrapyard can be checked (or alert authorities).

To sell them at the scrap yard. Gotta be careful driving in some countries; drive over an open manhole and you might crack an axle.

Isn't as easy to shatter in handling too, lacking stress concentrators.

My take is because the manhole is round.

The mouth of the 'hole' could be easily square, actually making a square shape is perhaps easier - since laying concrete is easier in straight lines.

So, most probably the shape of the cast iron cover (circular), drove the shape of mouth of the hole.

... fell for it like a dude trying to get his try at opening a stuck jar lid.