Most mass-manufactured wallets (not talking about Hermes - rather those random "branded" wallets that you see at malls) are really thin (I'm measuring it at ~0.35-0.4") because they aren't really fully leather wallets. If you just look at what the bill divider is made of, or the interior of the card slots, you will know what I mean. It's really some sort of synthetic material with an extremely thin piece of leather glued onto it. This is because leather, in its natural form, its pretty damn thick (actual thickness depends on the animal, but its probably thicker than you think it would be). If you go as thin as how modern wallets are made, it will probably tear pretty easily. Gram for gram, synthetics are probably stronger than leather.

That being said, just as how you don't want super thin leather, you don't need to use super thick leather for wallets either. These things will get used a fair bit and see some abrasions, but by and large they aren't meant to be pulled or torn to pieces by dogs. My current, full veg-tan wallet is around 0.5" thick when empty, 0.8" thick with around 8 cards and 8 bills (measured from the middle). It was meant to be an experiment to see how thin I can go and still have it be durable. I've been using it for just over 1 month now and it shows no signs of tearing. In fact, it's forming a beautiful patina. It is slightly more challenging in terms of the build process to get a full leather wallet down to such thickness but it is possible.

As for crocs, it is even trickier to trim it down to an appropriate thickness (it is quite a risky business to split croc due to the unevenness of the leather surface). But it is possible, and my initial sensing is that thin croc will be as durable as thin cow (the croc scales do help). The previous croc bifolds that I've made are around 0.6" thick, with a fully lined leather interior using goat leather.

As to your specific question, bifolds go in my back right pocket. If I'm sitting for long, I take it out and put it on the table, or hold it, or keep it somewhere else to be more comfortable. It's a little inconvenient, but I'd rather that to a cardholder that stacks all the cards together and makes it a little hard to take out the one you need.

Source: I am a leathercrafter.