And even then, they're highly simplified.
...
It's not integral to the flag's recognisability and it's way too complex
Let's look at some OTL examples (from wikimedia), beginning with Portugal
It bears both the cost of arms and armillary that are far more complicated than a counter charged cross. I would also argue that it these play exactly the same role as my cross with regards to recognisability. It was adopted in 1911.
Spain:
As with OTL Portugal, this COA is more complicated and serves the same role. Although designed in 1785, it was re-adopted in 1981.
The current Algerian flag was designed in the mid XX Century
I could concede that the crescent and star are simpler than cross I used, but I would emphasize the crescent and star plays the same role. However, removing it would not cause the flag to be confused with another.
What about the flags of some of the successors of Yugoslavia?
All three were adopted in the late XX or early XXI Century. Each charge is more complicated than my cross. They might add to the recogniazability of the flags, though the ordering of the stripes does that already. In any case, the details of the charges are not useful at a distance.
I'm not going to link all of the XX Century communist flags that added complicated seals that, with the exception of the DDR, were not needed to make the flag recognizable. I only mention them because the flags that replaced them are the only examples that are immediately obvoius to me as examples of XX Century flags that were simplified to tricolors. However, these changes were motivated by political, not aesthetic, reasons. And in those cases, the tricolors they reverted to were tricolors associated with romantic nationalist movements.
Edit: Italy also comes to mind, but the same applies.
Your design fits well, I think, a 17th-18th Century vexillological aesthetics, but for our 20th century, they're a tad too ornate.
I'm at a loss to determine to which XX Century vexillogical aesthetics you refer. As demonstrated above, there were many flags adopted in the XX Century that are at least as ornate as the flags I supplied.
Even so, I'm not sure why OTL aesthetics are even reverent. As I mentioned earlier, this Kingdom of Portugal exists in a world that never saw the rise of romantic nationalism nor atheistic communism. This should suggest a XVIII Century POD at the latest. In fact, the POD is late XV.