OK, let's put some meat on the bones re: bearing edges, most especially applied to classic drums - let's choose anything 3 ply or earlier single ply in good overall shape.
The reason rounded edges sound good on these older shell constructions is as much to do with the shell itself as it is to do with the edge. A modern multiple ply shell doesn't resonate so readily as these old designs. Modern shells equipped with modern sharp edges focus on attack & head sustain. Vintage shells concentrate on fundamental tone through shell resonance. Two totally viable but utterly different approaches.
Head sustain is largely only heard by the player. Without mic's, it doesn't transfer to the audience in all but the lowest dynamic of settings, & even when mic'd live in an amplified band setting, almost all of that head sustain is lost. Why? -it has no tone behind it. The drum tone you hear out front, the drum's voice, lasts for between 1 & 2 seconds only. That's the part where the shells are excited & contribute hugely to the satisfying full sound we all like our audience to hear. A modern shell with sharp edges also produces a fundamental tone, but it's shorter, & subservient to attack.
The edges on both types of drum constructions play to the strengths of those designs. Accordingly, because the classic construction shells already deliver lots of tone, head sustain is largely irrelevant. The rounded edges offer more head to shell contact. This delivers more excitement to the shells, but also puts the brakes on head sustain. The result, from a players POV, is a short but full sound, & that more faithfully translates to the audience. The modern construction player hears head sustain & relates that to "a resonant drum". Not the case. It's head resonance decay. The player hears it, the audience mostly doesn't, except for studio applicatios, & then anything is up for grabs in the processing.
So what does this mean in terms of the importance of edge condition? Simple, a rounded or typical vintage edge is much more forgiving than a modern sharp edge. As a vintage edge already puts the brakes on head resonance, a further slight loss, so long as good overall head to shell contact is maintained, has minimal impact on the drum's playing characteristics. A modern shell with sharp edges however, is utterly reliant on that sharp edge being as good as possible. Any deviation from perfectly sharp & perfectly flat will result in a pronounced reduction in head sustain, as well as increased tuning difficulty.
When thinking in terms of recutting edges, it's all about ascertaining what you already have, & balancing preservation of the sonic characteristics you want to keep, & those you wish to improve/augment.
Bearing edges - never has the term "don't throw the baby out with the bath water" been so aptly applied.