Is your town built on a giant copper nugget?
What you're trying to do is replace PEN with "the dirt". Dirt does not have the capacity for the task.
What is "the task"? It is to return imbalance currents. Remember, you have drawn the loads as three single-phase loads. As such it is not guaranteed that current is exactly the same on all three. Thus, you will have return current which needs to flow.
Now, Luiz Olivera has shown a method it can be made to work, by pushing voltage so very high (and thus current so very low) that the current is negligible and therefore the voltage drop across the dirt is bearable. This is called SWER = Single Wire Earth Return.
An example of fail
However, you want to do that at normal (safe in buildings) distribution voltages and currents. That's not going to work. In fact, we know exactly what happens when you try, thanks to the (North) American approach There, a hybrid system is used; domestically it's viewed as "Bonded TT" but the rest of the world considers it PEN with local earth spikes.
Homes in low density areas only get 2 phases from a split-phase transformer.
You see that we have set the stage for your theory to be tested. All that is needed is for something unfortunate to happen to that neutral wire. That's not a problem: Many homes have pole-to-home overhead supply wiring with triplex or quadruplex, and the bare wire responsible for carrying the weight is neutral as well. That whips in the wind for 30 years (aluminum has no fatigue limit) and SNAP! The wire breaks, neutral is disconnected, and we are putting your theory to the test.
And here's what we get. Yes, this happens often enough that it has a name: Lost Neutral. With no center neutral, the three (or two, often) line-neutral voltages wander all over the place. It's much easier to see in North American "2-phase" (really split-phase), because the two 120V legs are not 120V anymore, *but they still sum to 240V. They might be 110V and 130V. Or 100V and 140V. Or 150V and 90V. In the North American experience, the voltage doesn't wander terribly far, because that earth spike is making a difference. It is able to handle return current, just with very high resistance, which is tilting the voltages out of whack.
Obviously with split-phase, the voltage is a "see-saw". With 3-phase, it's more of a triangle-shaped see-saw with the pivot in the center of the triangle. More like a tug-of-war, honestly, with loads pulling on each end, and neutral where the ropes meet, but also tied to the center by a "bungee" stretch rope.
So it is not a good thing at all, no. The American experience is it can go for days or weeks undetected, simply because the earth spike is keeping voltages centered enough that things are not outright breaking. Loads are acting strangely, but they're still working, by and large. However this is still damaging to equipment when one phase pulls much heavier than another phase, causing the other phase(s) to have exceptionally high voltage. And that's what the local earth spike does for you.
Without it, you get a classic broken PEN, as discussed here by John Ward.
When it happened to us at my winter cottage, we lost a Crock Pot dish because it didn't get warm enough, and my sweetie said "I'm sorry, the toaster is very SLOW today". Toasters don't have speeds, so I was up out of my chair checking voltages and sure enough. The utility came out in an hour, on a Sunday, and fixed us and a neighbor with a lost phase.