That's a point I wouldn't know inherently.... But it only makes it worse...
As to the falling through... It comes pretty natural to be on the ice around here. It's a flat place that takes the easy way... A lot of times, the only place to go at all is on the ice, and some places the only time you can haul stuff in easy is on the ice.
And it's touchy business... Rivers and creeks, with swift water underneath... While it has to be slow enough for ice to form, the water underneath is still flowing enough that if you fall through you are not under the hole for very long. And you will play hell getting back to it too.
Normally you have a staff in your hand - similar to a shovel in a deep backhoe trench... You know you have a half second to get that shovel sideways across the top of that trench if it starts to cave in on you... Same thing. If your feet leave, the staff goes sideways in front of you and hopefully you catch it across your belly and only fall half way in... Hopefully you are pulling a polk and don't have a pack on... which is normal if you have a polk, even if you do have a pack, you put it on the polk on the crossings... And probably the most of your coats too..
I have likely gone through the ice a good dozen times... Mostly trapping beaver, but hunting too... Only a few of those were really bad and one damn near killed me. The real bad part is living through it. Once I fell in (not through the ice) in swift water, had to lose my pack and coat and snowshoes... Damn near killed me... And there I am, sitting on the bank, well below freezing, sopping wet, in shirt sleeves, with nothing but a folding pocket knife.
That was some learning, right there. That was way worse than every time (but one) when I fell through the ice. By the time I drug my sorry butt out of those woods and out to help I wished I had just died.
We carried our shotguns (what we hunted deer with where I grew up, using rifled slugs) at port arms for much the same reason crossing the tidal marshes. Sometimes what looked like good ground wasn't, as I found out one day. I stepped into one of those bottomless holes covered over with marsh grass, and the buttstock on one side and the end of the barrel on the other saved me from disappearing. I never felt bottom and went in up to my armpits, but pulled my smelly, soggy, self out using the shotgun as a bar across the hole. I was pretty miserable by the time I got back to the house, and was told all the way back about the 5 point whitetail that jumped right over the blind I was supposed to be in while I was up shivering by the Jeep.
I have to admit, I haven't crossed a lot of shallow fresh water on ice. Still, the big water has it's hazards, too. A friend went ice fishing on a big reservoir in Wyoming, drilled the hole through a couple feet of ice, dropped his line in, and it didn't feel right. So he took a flashlight and looked down the hole. The water was at least 30 feet below the ice....(they'd been letting water out). Needless to say, he got off the ice as fast as he could. I have heard tell of people getting out there on the Lake (Sakakawea) and losing a vehicle or losing ice houses they didn't collect in time, but haven't been mixed up in any of that, either.
On brackish water ice, our rule was simple: If the tide hasn't grounded it on bottom, stay off it. A boot full of ice water was one of the least fun things we could do as kids, partly because we'd have to explain how we got that water in the boot....and likely get out hides tanned for being out there.
But the ice tends to be thinnest where the current is strongest, and this fellow at Tulane has written up a decent explanation of things you have likely already observed the hard way. But I'm posting this link to the lesson that shows how to pick the most likely places for thicker and thinner ice, as well as what makes the bottom the way it is. It's more complex in any steeper gradient stream, especially with rocks, but the basics are here for anyone who wants to see them.
https://www.tulane.edu/~sanelson/eens1110/streams.htm It seems the faster water is also the deepest, or nearly so, as a rule, so that's two reasons to avoid it.
