I have one of these wallets. The one I have is an inexpensive "Aen Art" model from Amazon which looks exactly like the one pictured in your post. I removed the money clip as I don't tend to carry cash anymore.
The most obvious pro is how small it is. It forced me to prioritize the cards I was carrying due to the smaller form factor. It was amazing how many useless club cards/business cards etc. I was always lugging around in my previous wallets. Another plus is the durability. I've had mine for over 3 years and it still looks and functions as it did when brand new.
There are some cons as well. I find that occasionally it can be a bit of a pain to get the cards out when required, particularly those located more in the center of the wallet. To get around this I have placed my most frequently used cards on either end of the wallet to allow for easier access and removal. Another con is that the small size makes it hard to carry paper cards around. My home province is super cheap and still uses a paper health care identification card, and if the card is in the included sleeve it doesn't fit inside this wallet. I have the same issue with the insurance card for my private health insurance as well. I was discussing this issue with my functional medicine doctor who noticed I have this type of wallet, and he mentioned that he uses the money clip to carry cards which don't fit in the main compartment. Too bad I threw mine out several years ago.