A lot of shallow bodies of water have a lot of vegetation which helps raise oxygen levels.Also if the body has a lot of boat traffic with outboards the props and boat wakes actually add some oxygen.And largely the phytoplankton are responsible for the majority of oxygen content. But if the water becomes unbalanced then the fish can die.Generally speaking though shallow bodies of water can be very healthy fisheries.And the ones that have vegetation like moss and grasses and lily pads etc will hold the fish a lot of the time.
A good illustration of what can happen in unbalanced shallow waters is cutoff flood waters. When the Mississippi floods it leaves behind small ponds and lakes. Sometimes fish get cutoff in them.These waters do become depleted of oxygen many times.The fish have no where to go...and they die...beginning with the fish which are most sensitive to low oxygen levels like game fish.The last to die are the gar and bowfin and similar species which are tolerant of low oxygen.
On the flip side in the major river systems where turbulence and current mix the waters...fish can and are caught in the deepest holes many times.It's very common to catch fish in say the Ohio or Tennessee rivers (especially dam tailraces) in the deepest water there. If the current is swift the fish will position in holes in the bottom or behind some structure to get a break from the current.Very common to catch fish at times in 50 ft of water or possibly more. When I use to snag paddlefish below Kentucky Dam many times they were on or very near the bottom of the deepest water...since they are plankton feeders ...plankton have to be there and and I am sure other bodies of water have oxygen producing plankton at deeper levels which have to be producing some additional oxygen..because occasionally fish of a variety of species are caught at depths of 40 ft or more in lakes.But it does vary from one lake to another and time of year and other conditions.
This is all just my observations ...