This chart is scuffed but enough to explain what's happening OUTSIDE of simple chain of GCD casting. When the BLM has 3 stacks of one element, the next opposite element spell has significantly less cast time. and this exact 1 second cast allows BLM to minimize the loss of DPS caused by what's commonly known as "GCD clip."
On the left chart, it shows FIII recast time is 2.33s. However, the actual cast time is 1.69s because having 3 umbral stack significantly reduces the time you spend on casting. In other words, you would only spend 1.69s to cast a spell and have 0.64s of "free time" until you can cast next spell. This little wiggle room allows BLM to have a guaranteed slot to use an OGCD.
On the right chart, which is your rotation, does exactly opposite because default FIII cast time is 3.26s while your recast time is 2.33s. This means you're spending longer time casting FIII than you should. That's right, you're spending 0.93s longer. even if you could have casted FIV.
This means every 2~3 rotations repeated, you lost a cast of FIV and this is accumulative. By the nature of BLM, this is heavily consequential and the gap between standard opener and your proposed opener widens more and more.
This gap widens even more when you want to "weave in" OGCD like triple cast. In a super simplified manner, when considering this...
As you can see this in image, you are stuck at Triplecast animation and its delay causes you to wait even longer until you can cast FIV. Unlike that, the 1.69s FIII allows you to use Triplecast with minimized delay to the point it can be negligible.
It doesn't work as nicely as you think because, once again, your rotation does not have any room to use OGCD without forcing a delay due to OGCD animation lock. Of course, you can use xenoglossy or procced Thunder/FIII to weave an OGCD but you must understand that standard opener can do that as well. It's like comparing a gaining an advantage vs already having an advantage AND gain another. it's 0/+1 vs +1/+1.