Morning arowlands
This is all about achieving what is "reasonably practicable".
The guidance you quote says
the reception area is small (less than 10m2) and is of low fire risk
Working out what is "reasonably practicable" means assessing the level of risk and then assessing the cost of whatever mitigations in terms of time, money and effort and deciding at what point those costs are "disproportionate"(1) or "grossly disproportionate"(2) to the reduction in risk that would be achieved by applying each mitigation.
(1) Marshall v Gotham 1954 rarely quoted but in a higher Court and later than (2)
(2) Edwards v National Coal Board 1949
If it comes to legal action the onus is on the duty holder to prove that they had done what was "reasonably practicable" on the balance of the evidence - the so called reverse burden of proof.
Most of the time nobody bothers to work out what is "disproportionate" or "grossly disproportionate" but simply applies rules of thumb or what it says in authoritative guidance.
One of the rules of thumb is "Don't store things that can burn under stairs that form part of a fire escape".
Hence if you were to try and risk assess to permit this storage as described, you have your work cut out, not least since you could relatively easily enclose the storage area to make it fire resistant.
However, the risk is dependent on the numbers and types of people who can be expected to have potential need to use the fire escape - so the risk increases with population, number of storeys, vulnerability of users, amongst other variables including the amount and nature of stored materials and the volume of the stairwell.
I worked for nearly 30 years in an 8 storey 1930s listed building where there is a reception area with one/two staff at the Ground Floor foyer with residential accommodation on the top floor. Not much in the way of stuff to burn and the stairwell is vast, so anything that might burn at reception would produce relatively little smoke compared to the volume of the foyer and stairwell.
Contrast this with the situation where you might store some relatively easily combustible material under the stairs in a typical alternative fire escape route (EVEN in the 1930s building!) and you face the prospect of part or all of the stairwell rapidly becoming smoke logged.
So, I agree with Messy that trying to compare your scenario with a small reception area is not an appropriate comparitor.