Unless you vapourise the debris, you just turned it into chunks of smaller debris, travelling at the same velocity.

If you can ablate the leading surface (if the object is not spinning quickly, which honestly is unlikely) then the ejected plasma may push the perigee either into the atmosphere or at least to a higher-drag altitude.

...and this only works at LEO where, I hear, it is less of an issue.

Though it seems maybe still an issue, judging by all the shenanigans that the ISS has to do to avoid being shot down.

Actually, this works even better at higher altitudes because orbital velocity is tied to altitude.

It takes less delta-V to put a 1000km-apogee object on a collision course with the atmosphere than it takes to put a 400km-apogee object on a collision course with the atmosphere.