You pay electric bills for decades and it's never been more than around £600-800 pounds per annum which is below your threshold of something you get concerned about, then you get one for £2,000 having received an estimate of £400 a few months earlier. Being surprised is pretty understandable and not grounds for your disdain, I feel.
Most people, contrary to your post, do not check their electric metre every month, jot it down and do the sums - they being people with personalities and such.
Putting that the other way round, I could point out that that last remark about having a personality is rather offensive to those of us that have enough foresight, and cynicism, to keep a wary eye on bills.
I'm also a little curious as to how anybody, you or others, know what "most" people do in this regard? I certainly haven't seen any competently researched national polling data.
Personally, I've always made a point of keeping a brief check on such metered services, mainly because personal experience tells me that "estimates" always seem to err in favour of the utility company.
A few years ago I stuck a little monitoring contraption on the mains supply at the point of entry into the house which sends usage readings every x minutes to a receiver/display that then connects to a PC via USB and logs the data. So I can see instant or average usage at a glance, or from time to time, check the history data. There are several such devices available, ranging in cost from about £20 to £50 or so.
There's not much point in me quoting current usage costs, mainly because they're very close to £0 per year. With the new house, we spent rather a lot on energy efficiency, insulation, solar, ground source heat pump, storage, and so on. It cost a lot up front to do, but is environmentally friendly, will pay for itself over a few years and gives a considerable degree of independence both from energy companies and from the uncertainty of both future supply and prices. That system comes with pretty sophisticated monitoring and recording capabilities, precisely because such monitoring provides an early detection facility for system problems .... like a malfunctioning thermostat. It also sends me an alert if various trigger points are tripped, like out of range instant, daily or weekly usage. It just requires basic tuning of the trip settings.
It is not intended to be "looking down" but I really would suggest that some method of basic monitoring, whether it's that meter that lets you monitor current usage, a smartmeter or just monthly manual meter readings, isn't lack of personality but common sense.
With the smartmeter or the monitoring thing I had, you soon get to know what "normal" readings look like, and to recognise abnormal ones. For instance, if you have a base load of 500wH, or whatever, then that's what you'll use even if you're away, from things that are always on, like your fridge, freezer, PVR on standby, cordless phone base station and so on.
If it suddenly jumps by 3000w, and someone hasn't just done something to cause it, like boiling a kettle, then it should immediately cause you to wonder what the hell is going on. Like, is the immersion heater on constantly? If you're interested in cutting your bill generally, it can also help in identifying what devices use a surorising amount of unexpected power, like multiple older PCs on soft power down, or printers on 'standby'.
I think I have as much personality as most people, but a lifetime of running businesses where being
aware of what things cost, certainly at a macro scale, is essential to maximising effifiency and sometimes even to basic profitability, so I just have that sort of analytical mindset.
As for your original question, no, costs haven't suddenly jumped vastly to my knowledge, but immersion heaters are horribly greedy of power, in much the way that bpiling that 3kW kettle constantly would be. I would have thought that a thermostat failure leaving the immersion heater running permanently would have resulted in a very noisy hot water tank, and a burnt out immersion element. But a faulty thermostat would well have it running much to long, consistent with your overly hot water, and consistent with a bill, of that sort of size. And if so, and you can't find a sound justification for the utility company being at fault, I'd guess you're stuck with the bill. 20/20 hindsight is wonderful, etc, but the lesson, in my opinion, is to take an occasional reading and make sure usage is at least broadly within expectations.