They aren't inefficient. In the UK (paper ballots) an accurate estimate is available when the polls close, and a certain result is available within a few hours before next morning. This is much faster than US voting machines.
In US there were some laws that counting couldn't start before polls are closed. Despite mail in ballots arriving a month earlier. In some places they weren't even allowed to prepare them for counting (like verifying signatures and removing ballots from envelopes).
This is a good time to remind everyone that in the U.S. there are many different voting jurisdictions, and at the very least 50 different sets of rules. Some similar, some not. So it's difficult to generalize, some places count early, some not, some allow late arrivals, some not, etc.
1. You didn't have to count 151 million votes in the UK election
2. You didn't have to wait a few days for mail-in ballots that were delayed in transit to arrive
3. You didn't have to do this in the middle of a global pandemic that required poll workers to stay 6 feet apart
Generally the US election results can be predicted the same day, this year had additional challenges due to extremely high turn-out, high use of mail-in ballots, and limited number of pool workers due to pandemic.
In my opinion, elections should be done using paper ballots, and those ballots are counted using electronic tabulation machines. After a batch of ballots are counted, a random sample of them are selected and manually counted. Should the results match, then you can have a high certainty of the accuracy of the count. Electronic tabulation machines are actually more accurate than hand-counting, and by hand counting again, you reduce the risk of the machines making "mistakes" due to technical glitches or malicious backdoors etc.
That's actually pretty much on par for much of the U.S. We have paper ballots and results mostly finished before the next morning. There are stragglers, of course, for good reasons, but you don't really hear much about those unless they are possibly going to decide the election, like this year.
And then of course 2020 is it's own special kind of fun, not typical of any other year.
This year, my ballot had about a dozen individual races (including two state referendums and an advisory question) to vote on, and this is probably about or below the US median ballot complexity each presidential election.
But can you not return a presidential result in the first few hours, and then go back in priority order?
[Edited to add: 46 states have a lower population density than the UK, adding further logistical consideration]
If each community counts their votes... why does it matter how large an area they collectively cover?
St Ives constituency in the UK is generally the last to declare, presumably because the island populations are so small and remote it's considered unsafe for them to individually count and report the results for collation, for multiple potential reasons (Gugh: 3 residents)
Why is it about the US that means it takes a week... even with these machines which supposedly make it better?
If your count in the UK doesn't finish for a week, the parliamentary session opens, and you don't have local representation in parliament. There's an immediate procedural consequence that disadvantages the local area and may result in concentrated unrest.
If your count in the US doesn't finish, the relevant [Congressional] term doesn't start until January 3rd, 2021. As such, there's no immediately comparable procedural consequence.
The Electoral College doesn't cast its votes until December 14th.
The Supreme Court won't get involved, to hurry you up, until December 8th.
Correctly postmarked ballots will (in some states) still be counted if they arrive late, up to November 23rd.
Today is still November 15th. In theory, not all the votes have even arrived to be counted yet.
The US is vast. The political geography is different because the physical geography is different.