To start off, seeing maps would make this question easier to understand.
This is a Allied Situation map of the storming of Normandy. And here is another for the battle of the Bulge. As you can see they use a precursor of the now used NATO symbols often found in war games. With lines usually to show fortified areas.
The Germans however would use these. As you can see they use Flags instead of NATO symbols and 'blobs'. Another example.
The USSR however didn't even have flags. And purely relied on the 'blobs' and the name of the unit. Here is another slightly worse example. And another one.
That leaves me to question what were the reasons for the Allied forces to not use 'blobs'. Were blobs what were used before WWII even on the allied side (meaning were the squares developed during WWII)? And try as I might I could not find much Japanese or Chinese situation maps/military cartography. The ones I found of Japanese seemed to be similar to German/Soviet.
So yeah, I can understand the usage of blobs, units and brigades were often spread out and could be anywhere in the 'blob' but that leaves me to ask why the Allies used 'squares' with seemingly no easy way of getting a good grasp how spread out they might be or whatnot.
As a side question but what did the Soviet Union later use? Did they continue using the 'blobs'?
Edit: Oh and these might be helpful for other people to understand these flags.
So from a modern UK/NATO perspective:
The reason we use 'flags' is to keep it simple.
When a unit reports it's location, it reports the location of it's HQ (which will be the centre of mass for that unit). It takes a long time to report the whole frontage and depth of a unit, whereas to report the HQ location is quite simple - look at the GPS and send it up on the radio.
Now put yourself in the shoes of the higher HQ. Lets say you are a Brigade HQ (7000-8000ish troops) and you have to track 4-5 Battalions you command (600ish troops each) plus the logistical chain, artillery units, medical, etc. When the battle kicks off, the units are going to start moving and you need to constantly track their progress on a map.
If each unit sends in their HQ location as they move froward, it is easy to track. If they start sending in their whole frontage, their depth, where their sub-units (Companies/Squadrons) etc; then it takes too long to plot on the map. You don't have the time to do so, because the next unit is chiming in on the radio to give you a sitrep.
And if every unit sends this complex information, it clogs up the radio net. In battle, time on the radio net is precious. A HQ location takes 3-4 seconds to send and the higher HQ will already be familiar with the size of each unit - they will know roughly the frontage of a Tank Squadron, Infantry Battalion, or Armoured Brigade. It's their job to do so.
In the Army, we have a phrase: "Its better to have the 80% solution now, rather than the 100% solution when it's too late". This applies the NATO map marking system. Its not 100% accurate, but its good enough to make decisions in the fast paced wars of the 20th/21st centuries.
Since there have been no replies so far I would suggest to xpost this to /r/mapporn.