Covid Vaccine Rant

To vaccinate the population against COVID-19 it seems most governments have designed policies that involve phasing in huge groups of people at once. For example in California, on 4/1/2021 everyone 50 years or older will become eligible; on 4/15/2021 everyone 16 years or older will be eligible. 

My question is why are there set days for expanding eligibility instead of a priority queue (or something similar)?

The problem with set days for suddenly expanding eligibility is two-fold: If it's too early then the at-need won't get it soon enough before being overrun by others; if it's too late then you momentarily hoard a surplus and didn't get the general population vaccinated as fast as you could've. On top of that, once the less-at-need people become eligible, there is no way to prioritize someone who's more-at-need and didn't get an appointment yet. 

Why not just have a priority queue where the most at-need group gets first dibs on an appointment date, then lower tiers get progressively lower priority "dibs". For example, say in general appointments are available up to 10 days in the future. You could make 65+ able to book 1-10 days ahead, 50+ able to book 1-7 days ahead and 16+ only able to book 1-4 days ahead. So at first only 65+ can make an appointment for day 10, but as that day gets closer, more people can book an appointment for that day. Such a system seems simpler, more efficient, and more moral; in fact it appears to do away with the flaws of the current system without introducing any downside at all. So, is this a classic case of government inefficiency, or can someone come up with a legitimate reason the current system is preferable? 

(Implementation detail: In the very beginning, only the most at-need group is eligible to ensure they fill up all the appointment slots. After that, everyone 16+ is "eligible" but of course the less at-need groups will be lower priority and will be unlikely to see any open slots until the more at-need groups have been fully vaccinated. As the more at-need groups become more vaccinated you can tweak the numbers of allowed lookahead days to give the less at-need groups more freedom to book in advance. For example, after most 50+ are vaccinated, then they only get first dibs for appointments 9 or 10 days in the future, and everyone else can look at days 1-8.)