A factor to bear in mind is that it is a contractual issue (rather than a VAT issue) as to whether amounts are quoted on a VAT inclusive or VAT exclusive basis.
As an example with easy figures, a charge of £100 "plus VAT at the applicable rate" would change from £100 + £20 (20%) VAT = £120, to £100 + £5 (5%) VAT = £105. This gives a £15 refund to the customer.
However, a charge of £120 "including VAT at the applicable rate would change to £114.29 + £5.71 (5%) VAT = £120. This gives no refund to the customer, leaving a £14.29 benefit of the VAT rate change with the supplier.
As HMRC's posts have mentioned, it is for the supplier to decide whether to apportion charges that cover a period that crosses the rate change. Clearly suppliers are more likely to do this where the contractual position leaves them with the benefit, as in the second example above. You would hope that they would still do so in the first example, as it benefits their customers. But it creates extra work for them, for which they would receive no direct benefit.