Once you stop fighting to stay dry, you are completely liberated from that fairly significant mental effort. If I do a packrafting trip or I’m going cross country along the coast with swamps and river crossings, I just say f**k it and hop off the airplane floats into the ocean at the start or find the first puddle, stick my feet in it, and get it over with. If I’m doing a high country trip where there is a decent chance I can stay dry, I will work towards that end. So my strategy is based on the likelihood of success. You probably fall into the “get wet and get it over with” category.
Not that this strategy is without its downsides. Your feet will be colder, no question. That’s a deal killer for many. Putting wet socks and shoes on in the morning sucks. Some people’s feet fall apart if pruned all day. You need to practice good foot care in the evening and sleep with dry socks/feet to allow them to recover.
Inov8 makes some minimal shoes with seriously aggressive tread patterns like the Mudclaw. Those, with some medium cushion synthetic socks (for instance Coolmax crew height) and some very light gaiters to keep some crud out, could add up to a viable strategy. But definitely do some day hikes with wet feet to see if you are okay with it before committing.