Last week I took someone to Wanchai at 8:30am, and they were refused walk-in, being told it was no longer possible. The staff member advised them to open the online booking webapp before midnight and then keep hitting reload until a vacant slot appears.
Trying this, it seems like a slot occasionally appears after, say, 50 reloads. However they seem to disappear very fast, before it's possible to click through and book.
Furthermore, sometimes it offers slots in the past, e.g. 13 March 2023.
The whole process seems pretty insurmountable. Though I imagine at least this could constitute a defence in court, if someone were to be prosecuted for not obtaining an ID card within 30 days, as normally required by law.