thats a very good way to get passengers to fly via a different transit point and airline- instead of having good tourists who travel in prem cabin and spend money in the city. (alternative is either spend money at regal or get tired before anything opens in the city)

all they need to provide is a reasonable space for people to hang around for 3-4 hours. the BA arrivals lounge has 50ish shower pods + lounging space.
if people dont have to wait for 2-3 hours or spend usd100s for a shower, many people will not want to clear transit security for this.
or the alternative is to accept their operation sucks and have someone at 0830 or 0930 to bring transit passengers back to arrivals from the Wing.