I use a shoulder bag (man purse) for small stream fishing. Mine is a 12” wide canvas British job, similar to that useless minuscule top photo you posted. ;-)
A couple of things:
1. You will probably want a shoulder bag on the opposite side of your casting hand, but it will drive you nuts unless you swing it around almost behind you. However, IF you catch fish and are wading or fishing from the bank and have to bend over to release the fish, it will slide back in front of you and drive you nuts.
For that reason, I always use mine in conjunction with a belt with a couple of small pouches around my waist. One of those pouches holds my wading staff. That pouch is located at the 8:00 position on my waist belt. When I swing my man purse behind me, I position it on the other side of the wading belt pouch. The wading belt pouch keeps the man purse from sliding in front of me when I bend over, but doesn’t prevent me from positioning in front of me to get stuff from it...
...problem solved!
It doesn’t have to be a wading staff pouch, it could be a water bottle holder or whatever and it doesn't have to be a separate belt, but you get the idea.
2. A proper fishing bag has a WIDE shoulder strap, 2" minimum. DON'T buy one with a narrow strap, even if it has a shoulder pad. You'll be sorry if you do.
Shoulder straps that are sewn to the bag are usually more comfortable and lay better than those that attach to the bag with with clips and there is nothing to break. But straps that attach with clips allow you to easily slide something on the shoulder strap if you desire. I have a pocket knife in a sheath on my shoulder strap. I figured a way to attach the sheath even though my shoulder strap is sewn on, so a nondetachable strap isn't a deal breaker, juts a narrow strap.
3. British style or messenger type bags usually have one single large compartment and two pockets for fly boxes. Those pockets are for standard size fly boxes. If you have big fly boxes, they won’t fit and you will have to put them in the main compartment along with everything else. Finding smaller fly or lure boxes will solve that problem, IF you can find the right boxes.
Cabela’s used to sell a great cheap clear 7” long box that came in everything from undivided to 10 compartments. I use them for my bass flies and even lures but of course, I no longer see them on the Cabela’s website.
Dewitt Plastics makes great boxes but you’ll have to decide what you want and then find someone who sells them.
4. Another problem with an over-the-shoulder bag with a single main compartment is, with fly-fishing comes gadgets so you have to dig around for things you might need which is pain if they are small. For that reason, I designed an insert for my shoulder bag that the manufacturer fabricated for me to hold the small items I carry...
...problem solved…for me.
However a bespoke insert won’t be an option with 99% of the single compartment bags out there so you will have to figure out another option to separate items or you will spend all your time digging around for stuff.
5. You will also more than likely have to come up with a place to attach a pair of nippers, pliers or hemos, tippet, etc. unless you want to dig around for them all the time. I hate dangling stuff so I keep that at a minimum.
6. What about rain gear, a net and other stuff? If you want to carry that all the time or just on occasion, you will have to put it in the bag. Will it fit, or will you have to figure out something else? I use the waist belt with pouches I mentioned earlier for my extra stuff so my shoulder bag doesn't end up weighing a ton.
The bottom line ONCE again is to think things through before you start buying or expect to buy over & over again until you find the right thing, which is a waste of time and money.
I'll say until I die, patience is a virtue when it comes to choosing fishing tackle...
