Over the years, the eternal question "what do I put on after electrolysis" is always front-and-center. I tell my clients that my only worry is actual post-treatment infection (from an outside source). In all likelihood the tiny electrolysis wound is closed within 24-hours and I suppose products can be used without much danger.
The risk, however, is real if a person self-doctors with something that is contaminated with bacteria. Slathering contaminated products on an open wound would make matters much worse. "Hands off and no products" for 24-hours makes sense to me. And, that's what I recommend.
Of course, "soothing the hot skin" is fine; but I don't put a lot of value in short-term "results" that are based on a client's opinion. To see if any product actually did something to make the healing better, I would want to examine the skin a year after treatment: one area with, and one area without the product in question. I don't think there would be any difference at all.
What I know for certain is that clients (and electrologists) are absolutely going to continue using products, experimenting with products and recommending products. In the long run, the skin will heal just fine, even if the product was detrimental to healing. You can't stop the healing process.
The only product that I have observed making an objective difference is pure emu oil. But that's another story and, truly, not worthy of discussion. Besides, it STINKS and no woman would ever use it.