Think I have got this right but please let me know if it’s wrong
If I trade my car in on the middle of the month they charge you for that month so they get about £20 and refund the rest,
The seller also loses about £20 and also gets a refund.

The old system did let you drive till the tax ran out as I have never seen a seller ark for a refund.

I have just bought and checked on the DVLA web page and it states that I am still taxed till November.
Sadly I cannot use any of this as it will cancel at any point even though the seller will still be charged the full month.
They say they are losing money with this scheme – sure they are.

Yep, you do have it correct.

When I bought my RRS recently, I had the added hassle of finding a post office near the dealer, that would tax it, before I could drive off.

I do understand that it's to stop the (often used) ambiguity of whether the car is taxed, when you buy it, but still...

This new system is all wrong, the car is taxed and legal, however when the owner sells it, it ceases to be, so this must mean that the owner is taxable, and not the car.
But the DVLA wont have it, so everybody loses out 07,TDV8,Black, Black Heated leather all round, Rear Entertainment with Headpones & Remote, TV, DVD, Pure Dab Digital Radio, Sidesteps, Adaptive Headlights, sunroof, now working fuel burning heater )))

Anyone who buys a car now is driving illegally till they tax it, this is just daft you should at least get a bit of time to get the paperwork sorted out without getting in trouble.
Even a day would help, at least that would let you can get home and have a chance to get online.

Bought the wife a car recently. Admittedly, it was SORN'd, but took the iPad with us, bought the car, and taxed it there and then to drive it up the road

It's still a system though...

The new driving license system is also ridiculous. They get rid of the paper counterfoil and replace it with a system that requires everyone involved to jump through digital hoops when hiring a car.

I can understand the push to making official systems digital in nature but the new system is the equivalent of buying a new computer and then having to set up a water wheel to power it. 2012 SDV6 - it's missing a couple of cylinders
2008 TDV8 - it was a labour of love and is much missed