Felt Soles, Studs, etc.
Felts are best for defying the otherwise oil-like slickness of algae on hard surfaces like rocks, but as mentioned are not as durable as cleats. There are velcro strap-on cleats available that are carbide screwheads (not corkers) and their light weight makes them easy to carry along for rock hopping without burdening your longer walk on the sand. Aquastealth is popular and offers a great compromise between the grab of felt and the go of normal cleated boots.
On the beach, I use neoprene divers boots because nothing in the world can compare for comfort during long walks on sand. These are worn over gore-tex, neoprene or my OS Systems molded drysuit-type stocking foot waders. I got a pair of Teva-like sandal cleats that go over them when needed, chosen over the corkers because they are light and easy to pack - like a pair of beach sandals.
One note about Aquastealth when used in rushing freshwater streams - they are no where near as effective as studded felt soles. I wear Danner studded felt soles in summer and fall after dislocating a finger by slipping on the low water stones by the streamside one fall. My partner, an Aquastealth enthusiast, and I were crossing a rushing tailout about thigh deep and hitting hard on the legs. With a wading staff I made the crossing depending on firm footing with no chance of backing up. Watching him, I yelled that he should not make the crossing because he was not able to retain footing, which tenaciously denied for several tentative minutes before finally retreating with great difficulty. You gotta have carbide studs and felt
around low water in fall, and he completely agreed. Knowing the limitations of rubber material on slick algae covered bowling ball rocks in a knock-down current is key. There is no free lunch, although the new-tech soles are a great compromise between cleated and felt soles, they are not the solution to the demands of slick river wading.