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Here is my invention for you.

It is a board. The pliers and snips that volunteered for this project straddled it nicely. If you cut off the ends of the board and reattached them at right angles (with glue or a screw) so it looks like a letter I it would be steadier than this one, which was propped on the 2x4 back there.

The little red pliers did not have legs as heavy as the others and so wobbled a bit. You could cut a notch in the top for any like that.

How about something like this?

https://www.amazon.com/Olsa-Tools-Pliers-Organizer-Storage/dp/B01M27BV34

If you want more ideas then run a Google search for "plier rack"

The problem is you are using office supply organizers for tools.

Try hitting one of the Borgs (Home Depot, Lowes or Menards) and visit their tool section. They should have plenty of tool organizers. Be warned: they won't work very well on office supplies.

You say hanging them on a wall is acceptable. In that case:

Put them against the wall.

Grab one at your nearest toolshop or hardware store or make one yourself. All you need is a piece of metal/wood, stick it to a wall and put screws, nails, clips or other objects in it to hang your tools on. The boards with pre-fab holes in them are pegboards.

I use a grey foam block like is typically used for packing or cut out in shape for instrumentation cases:

I use an X-Acto knife to cut out slots for the heads of the tools that roughly contour the shape of the head, but slightly smaller for a snug fit:

This provides immediate access to my most commonly used tools, with each tool having it's own location to assist with muscle memory, while keeping all sharp edges(including said X-Acto knife) properly protected. While I could secure the foam to the desk or weigh it down, the weight of the not-currently-being-used tools in the foam is significant enough in my situation to not require additional weighing or securing.

I would get a board (of ply or similar) and lay out the pliers etc in a sensible arrangement. Then insert a screw for each tool so that the tool sits on the screw by its hinge when the board is vertical.

Probably cheaper than buying a board that may be larger than what you need...

You could also add elastic across the handles and make it so the board is self supporting, which means it could be stored under or to the side of the desk, if your desk surface is at a premium...

Here's yet another tools-on-the-wall idea. This is light gauge galvanized sheet metal -- probably 24 ga from the HVAC duct aisle at the local big box store. The non-magnetic tools (flux pens, tweezers, etc) have a magnet bonded to them with epoxy; the magnetic tools have a magnet epoxied to the steel sheet instead.

Typical is a wall rack with holes in which one part of the handle is inserted. Wooden home-made or wire/plastic for pegboard mounting purchased. If you want it on the desktop rather than wall-mounted, then a stand supporting a board which has holes drilled along the edges.

Some results (unlike those) I have not seen in person show up when I put "plier rack" into google...

You can get hard wire cutters that cut hard wire without becoming junk, BTW.

Personally, I mostly use a clear zip pouch system (which was perhaps intended for fishing tackle) that I picked up surplus.

It looks like there's a window behind the desk but you mention a wall so as others have mentioned, a pegboard is a cheap and simple solution. Make sure you mount it with spacers behind it so that you can actually get the accessories in. These 'plier holders' are perfect for this:

They are less than a dollar each. The tool goes in business-side down.

If you want something that you can place on the desk I would go with something like this. If you can't find something like it you could get small piece of 3/4 inch plywood and fashion it yourself with some basic tools.

The 'window' cutouts on the side are for aesthetics and purely optional. The big advantage of making it is that you can customize it exactly to your needs.

If you aren't sure how to go about making something like that, reply and I can provide more detail.

In lean manufacturing circles as well as aerospace vehicle maintenance an accepted way to deal with tools is with foam cutout tool trays, either canted near the work surface or hanging on the wall. Google for "lean foam tool wall" etc. You'll quickly see that Fastcap's company founder has produced a bunch of youtube videos about this -- here are a couple of hits from an images search. (Not affiliated with the company -- I do buy foam from them though. I got infected with the tool foam practice myself while in the USAF.)

Many years ago my father just drived a pretty big nail to wall, near the table. You can easily hang big/small pliers on it, they're pretty stable and easy to access.

Pegboard, or a magnetic tool holder (Harbor Freight sell those for only a few dollars)