NO.
My design QC tool post. As you can see, I used SHCSs. The stainless ones in this early photo had rounded ends (more below) but they were softer than HSS so they mushroomed. I removed then before they became so big that taking them out would enlarge the tapped holes. The stainless looks nice, but I replaced then with high grade, black oxide cap screws. The cap screws are hardened and work just fine.
On the tips of the screws: I gave it some thought. Cap screws usually come with ends that are the result of the rolling process that produces the threads. Normally nothing is done to them after that so the ends are somewhat irregular. I did not like that as it might move the tool bit as it was being tightened. While a flat, dog point may be the ideal tip, it would be hard to make in my small shop. So I choose a tip that provided contact at a centered point but was somewhat broad. This was a rounded tip with a large radius. I made these tips by first putting a chamfer on the screws and then working them on cloth backed sand paper that was backed up with multiple layers of soft cloth so it had some give. A few dozen strokes while rotating the screw in my hand produced a nice, large radius curve. And the high point was in the center so it did not have much tendency to move the tool bit as the screw was tightened.
The only advantage that I can think of for the set screws is that they take up less space so more holders can be stored in a smaller space. That does not make much difference with my holder design as they are somewhat large anyway. A definite advantage to the SHCSs is that the Allen socket will be larger than that on a set screw of the same thread size so it will last longer with use. I don't know how many set screws I have had to replace because the Allen socket either wore round or that area just split apart.
If you are curious about my shop made, QC tool post, which I believe has significant advantages, you can get the plans here:
Quick Change Tool Post for Lathe - HomemadeTools.net
I've replaced a number of the cheesy tool holder set screws with regular USA hex cap screws. Is there any reason to use set screws?