Can we please put this one to rest. Boots of whatever material that fill with water will not "drag you to the bottom" The water inside the boot/wader has the same density as the water outside. They do make swimming a pig but provided you are wearing your pfd you will still float fine.
One of the biggest problems with chest waders in rivers is quite the opposite. They tend to hold air, lifting the feet and pushing your head down if not wearing a pfd or causing you to double up, butt down if you do have a pfd on.
As mentioned the real problem is getting out of the water. It is a lot of effort but the best thing is to take them off if you don't have the option of crawling up a shallow bank.
The comment about concrete overshoes was hyperbolic, water filled waders are obviously not concrete filled waders.
I wore hip waders for years while duckhunting and sneakboating in a canoe, since my preferred technique was to drag the canoe through the marsh into large potholes where jonboats could not venture. I had never before had a swim while wearing waders.
In that particular swim I was not paddling or even getting into a boat; I was officiating at the start of a canoe orienteering event and wearing hip waders while helping participants into their canoes. I was not wearing a PFD.
When I slipped off the high marsh bank I went completely under.
Surprise #1, it took an enormous effort to claw my way back to the surface without being able to employ any leg kick. Actually swimming any distance would have been near impossible without a PFD, and challenging with one.
Surprise #2, I could not get back up the bank without assistance. The hip waders were fastened to my belt via narrow straps run through metal ladder locks on the sides. A sensibly way to keep the waders up and secure,
unless they were filled with water.
Getting the waders off would have required using both hands to undo the ladder locks. That was a tidal river with some current, and there was no way I was letting go of that suddenly beloved Spartina grass on the bank. I was about to undo my belt and lose my pants when my laughing companion realized that I was truly struggling and pulled me out.
Had the hip waders not been fastened I think I would have been able to kick my feet and legs free; in that scenario chest waders might be more of a challenge.
Take away #1 from that eye opening episode was to never again fasten the waders using the ladder locks.
I have (unintentionally) swum while wearing Mukluks on several or more occasions. Actually swum, some distance with some leg kick, and usually poured no more than a cup full of water from the boots.
Take away #2, kind of like doing a test swim with a PFD or drysuit, it would be a good idea to do a test swim while wearing waders, or any kind of large over boot, if only to evaluate the swimming and extraction difficulties. It would be a shame to lose both your boots and your pants while tripping.