No not a wire edge. I was talking about the excessive arching that leads to a steep angle at the edge, or too much pressure which causes the pastes to coarsely. Just as with stones, if you use a lighter touch the abrasives cut more slowly and finely; use too much pressure and they cut fast and coarse and create a duller edge, even if the final angle is ok. The trick with pastes is that the more flexible or compressible your substrate is, the more careful you have to be about being consistent with your pressure (and tension on an hanger), because they tend to put more pressure on the edges of the bevel than the middle of the bevel, cutting those areas faster and leading to the arched bevel shape. A little too much slack and you've got a very steep cutting bevel and you may have to remove a lot of metal to get things back into shape so the pasted strop will contact the edge under normal circumstances. This may be another reason why pastes have gotten the reputation of only working for a little while - one slip in your technique and the bevel is so arched that it will take a bunch of laps to get the bevel back to where it was. Since stropping is so "easy" the obvious explanation is that the pastes aren't working anymore and it's time to hone, when really the issue was a slipup in your stropping technique. This is what I found when I went to a really hard incompressible substrate, that the pastes didn't "stop working" with lots of honing, even if I got a bit sloppy or careless.
I vaguely recall being worried about overhoned edges from pastes back when I first started, but I don't know if it was something I ever experienced myself or just heard about and repeated. But I don't think I've ever gotten a wire edge from pastes myself, and Verhoeven never seems to have gotten them either in his honing paper. So there may be some particular set of circumstances that cause this to happen with pastes. I'd be curious if you can fix this with a bit of pyramiding on the pastes. Although pyramiding is a bit more of a chore on pastes because of the cross-contamination issue.