Like you I use my postal vote. In the UK, apart from some of the more outlying places, the counting is normally completed within 24 hours of the close of the poles, and none of the counting is done until the close of the polling stations (and some places take great pride in getting their results returned in the shortest possible time - various tactics are used, but primality it is using a small army of counters who have done a lot of practice and very careful choice of the location to do the counting making sure it is very accessible to the local transport network.

I find the way the some states do their counting is, in my eyes, somewhat dubious, if not worse....

This article on Sky News might give some of the answer to your very sensible question.
https://news.sky.com/story/covid-19-vaccine-how-exactly-does-the-cold-supply-chain-work-12149118

One thing to note is that there is no indication that the smallest "delivery batch" needs to be 1000, that is the size of the smallest package, not the actual number of doses in it.

(I'm not sure why Sky chose to choose the Isle of Arran, it is remote, but by no means the most difficult population centre to get to - try the Isle of Barra in winter, I've been there when no ship, boat or aircraft could get in for over 48 hours. Strange off-topic comment - The little hospital on the Isle of Barra is one of the many I've ticked-off on my "Visited all UK hospitals list" :-( )

Either dubious or disorganised

I'd go for "both".
There are perhaps a few places that make it geographically difficult to do a "proper" count in a sensible time and manner (Alaska comes directly to mind) but for the vast majority of the land mass of the USA there is very little reason, only (in my book) lame excuses.

In evolutionary terms we should let some of us die off, then the rest will be stronger. But oh no, we have to protect the weak so future generations will need even more protecting.

That is an over-simplistic Darwinian view. A more nuanced view comes from Adler's branch of psychoanalytic theory which posits that all human behaviour is ultimately aimed not at individual survival but survival of the species which includes ensuring the weak survive for various reasons.

Our Gov says they can start vaccinating on the 4th of January.
But!

Initial vaccinations should be done by general practitioners and they can't do this because the vaccine NL has chosen requires it's cooled at -80C at all times until used, and the GPs just don't have the equipment. But if they were able to do it, they'd have to vaccinate the elderly and handicapped, plus some of the nursing staff. Then further down the line all people 60 and above will get it, plus the rest of the nursing and caring staff. And then somewhere around August 2021 will the rest of the population be applicable to get their jab.

Funnily enough, our vaccine comes from the UK, is made at Oxford University. It'll probably cross your vaccine coming from Belgium. Can you still follow this?
Oh and ours has a coverage ration of anywhere between 50 and 70%. So not the best of vaccines either. Although by sheer coincidence (read: they made a mistake in administering the dosage to half the test group) they found that if people get half a dose one month and a full dose the month thereafter that this increases the coverage of the vaccine by a lot.

That's odd. We're being told:

Our first vaccine is commonly known as Pfizer, has been approved, is made in Belgium, and has all the problems of low-temperature transport and storage that you list.

Our second vaccine is expected to be Oxford. That hasn't been approved yet, but has been submitted. It had the dosage error in testing leading to the 70% - 90% coverage variation that you describe. But it does not have the low-temperature storage requirement, and our GPs/care homes are eagerly awaiting the simpler roll-out.

Looks like your GPs are being given a mish-mash of those two stories. Maybe our Brexit misinformation team are trying to put you off buying any, so we can keep it for ourselves?

No, that's true. I mixed it up. Have looked it up and the Oxford vaccine can be kept for 6 months at 2-8C.
At least the world has a problem because those taking the Pfilzer vaccine require the -70C cooling and only a handful companies in the world make these highly specialized freezers, one of which is in NL. They're running at top capacity.

Each government has made choices, and some of they were made a long time ago before there was any idea of the delivery schedules.
The UK government, like the Dutch one, is sourcing different vaccines from different developers, and it just happens that the Pfizer one is coming to availability ahead of the others, they've only ordered a limited number of doses (if one can call a few million "limited"). It wouldn't have taken much of a change in the testing programmes for the Oxford vaccine that the Dutch have selected as their "first call" to have beaten the Pfizer one into use. From memory both governments announced 3 or 4 months ago they were ordering a number of doses from each of several potential vaccines and that the final shipment dates would be highly dependant upon the outcome the the then very early stage testing.

The effectiveness figures are not as simple as "50%" (or whatever the low figures is), due to the way the testing was done. Indeed, due to the testing dose errors it has been found that the effect of the Oxford vaccine can be enhanced to >90% (similar to the Pfizer one) by not giving the same dose twice but giving one "big" dose and one "little" dose (I can't remember the sequence), but giving the "standard" dose (the "big" dose) twice is not as effective, being down to the lower figures quoted.