> So, if leapseconds are actually painful for you, then maybe we need to contemplate making this kind of adjustment on a finer timescale, like milliseconds.

That is what a lot of organizations do, "smearing" the leap second since they know their systems can't handle the discontinuity. I think this shows that software has failed in general at handling leap seconds correctly. As another said, I think leap seconds are unnecessary complexity with the frequency at which they happen.