“In their defence, riders told us they do try to pick up after their horses,” added Mr Hall. “Though in some cases it’s not practical”.
I think this referred to going back after they had ridden to remove droppings - which is an option, often employed by responsible RSs and large yards using shared spaces.
It is impractical, rather than impossible for many horse riders to dismount mid-ride. It is also a significant added risk - not just for horse and rider, but for any pedestrians or car drivers who may be adversely affected by a loose horse rampaging through the streets - frightened, runaway horses tend to come with a side order of collateral damage.
Most responsible riders take measures to reduce the risks their horses pose to those around them when they take them out - training, exposure / experience building, using suitable tack to control the horse, wearing hi vis etc - and of course having insurance to cover any damage is anything goes wrong. One reason horse riders are defensive about the idea of picking up poo is that it increases these risks, as horses are more easily controlled from "on board".
For an able bodied rider with a well trained and sensible horse, that risk may be small. I think it is arguably reasonable for those riders to jump off and kick poo off a shared path like the OP described. For other riders, it would be more sensible to return at a later time without the horse - if it were deemed necessary to remove horse droppings from that area at all. It would partly depend on the accessibility of the area, and the nature /use of path.