Haithambadawy -
First, let me clarify that I'm not all that familiar with what CSI / SAFE is doing for their punching shear calcs. My thoughts here are more generalized based on what I have seen done in RISAFoundation and RISAFloor ES. My educated guess is that CSI is doing something similar, but I can't claim special knowledge on this.
In concept the idea of looking at shear stresses from an FEM analysis instead of directly looking at the forces and moments is valid and rational. However, I don't think it is easy. To me it's the type of thing to do for a PhD project where you want to propose a change to the ACI formulas on how these stresses are calculated. You build an FEM analsyis and see what stresses are produced in your simulation of reality. Then eventually you test it out in a lab to see if the reality matches up with the FEM results. But, this is not something that you would generally do as a practicing engineer.
Some reasons to stick with the force and moments and then calculate the punching shear stresses from those:
1) This is what the code tells us to do. You can argue that the direct stresses might be more accurate. However, you're going out on a bit of a limb. If you're coming up with more conservative results using the direct stress method, fine. But, if you come up with less conservative results then it would be very easy for another engineer (or plan check engineer) to state that your design did not meet the code requirements.
2) The code calculations are based on an assumed punching shear perimeter. Actually, multiple punching shear perimeters (edge, corner, or such). The reality is probably different than what is assumed in the code. It's just been demonstrated that these perimeters give reasonable results when matching up with test data. But, what sort of perimeters are you going to assume when you look at the direct FEM stress results? Using the code perimeters may not always be the right way to do it.
3) What direction are your local stress results reported? Do these line up with the assumed local axes of the punching perimeters? You can probably make it work if they don't, but it will be more work.
4) Is your mesh fine enough to capture the variation of stresses along these elements? Because you're not concerned as much with the average stresses as you are with peak stresses. Right? So, you have to be careful with your model to make sure you can adequately capture the variation of the stress and arrive at a reasonable peak stress at one corner or edge.