what is the reason not to put the strings in parellel?
The forward voltage drops of LEDs are not all the same. You could wind up with twice as much current as you planned through one branch, while the other branch has almost zero current.
And I dont see how your circuit is constant current. There's no feedback loop or regulation. Does the NFET do the regulation?
Look at the rightmost simulation, where the gate voltage is held at 5V, same as a logic high from the MCU. I vary the supply voltage to see what influence that has on the LED current. Note that when the supply voltage is more than 22.8V, the current through the LEDs is very constant. Look at the Port (gate), Source and Drain voltage to see how the NFET works to keep the voltage at it's source constant, which means that the source current is constant, which in turn means that the drain (LED) current is too.
For a fixed gate voltage (5V is what I am assuming), the LED current is determined by the Vth of the FET and the source resistor R1. In the rightmost simulation, I picked R1=4.7Ω, which makes the LED current ~520mA, but you can make it anything you like by changing R1. The leftmost simulation shows the LED current for values of R1 of 3.3, 4.7, 5.6, 6.8, 8.2, 10, 22, and 33Ω, while the supply voltage is swept as before. Note that once the supply voltage is big enough, the LED current is remarkably constant.