So yes, I do see this (Result: color profile has not been embedded, remains untagged). But there is also a fundamental issue in the steps. Open untagged RGB PNG fine. You really now should Assign the Working Space to that data and then convert to sRGB.
Then save, and if you reopen it, the embedded profile does stick.
However, what you report isn't what I'd consider correct or ideal! The untagged image should be assumed to be in the RGB Working Space you have selected in your Color Settings. In my case, that is ProPhoto RGB and that is used when I try your steps and then convert to sRGB. Of course, if the data isn't in ProPhoto RGB, this 'assumption' leads to very ugly color.
I'm going to vote it a bug, the product shouldn't (not) embed the profile after a conversion. Good catch. But it might be worth testing whereby you do this:
Open Untagged RGB PNG image
Edit > Assign Profile... > sRGB (if that's the right profile for the data).
File > Save
File > Close
The team needs to know if, like me, this works for you and then maybe they can explain if using your steps (Convert from Untagged) is an excuse for not tagging the data (I think not).
Author “Color Management for Photographers" & "Photoshop CC Color Management/pluralsight"
Good call, thanks for mentioning those other conversion options. So far I have tried:
Edit > Convert to Profile...
Edit > Assign Profile...
Turning on Missing Profiles - Ask When Opening in Color Settings
Assign working RGB
Assign profile
For each of these options I've Saved, Closed, and Re-opened the file. The color profile remains unembedded for every possible route, and always remained Untagged RGB on re-opening!