A birthday is a legal timestamp. A car crash is a legal timestamp. When the time is off by a minute, these events can’t be catalogued correctly any more.
Shifting the timezone by a couple seconds does not prevent or hinder cataloguing events in any way whatsoever, certainly not more than switching to daylight savings time does or the mere existence of timezones, which may easily be half an hour or even more off from the solar time - the offsets we use for time are effectively arbitrary already, and adjusting the arbitrary choice of the offset by some seconds is not a fundamental difference. Event timestamps already map to different days depending on different timezones, you do need to know which timezone your clock is using, of course, but you already need to do that.
For people born just around midnight, especially around new years eve, a few seconds could impact their DOB by a whole year. This could affect everything from university applications to boating licenses to social security.
Some countries have boating license laws that are different depending on whether your DOB year is >= 1980, as an example for this type of "grandfathering cutoff".
Maybe you seem to think that was is being asked for is to retroactively remove leap seconds from UTC? That is not the case, all that is being called for is to stop adding more leap seconds.
Both can easily be placed on same monotonic time. Actually makes a things simple. You don't end up having 31/12/1972:23:59:60 and wondering why is there 60 there...
Shifting the timezone by a couple seconds does not prevent or hinder cataloguing events in any way whatsoever, certainly not more than switching to daylight savings time does or the mere existence of timezones, which may easily be half an hour or even more off from the solar time - the offsets we use for time are effectively arbitrary already, and adjusting the arbitrary choice of the offset by some seconds is not a fundamental difference. Event timestamps already map to different days depending on different timezones, you do need to know which timezone your clock is using, of course, but you already need to do that.