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It's not so much whether there's a better-thought out solution as whether there's a solution at all.
If you want anyone to get through, people on motorbikes will generally be able to get through, as they will fit through most kinds of person-sized gap. In Trinity Street, many (I assume) will simply hop onto the footway, as per the blue line, unlawful though that is. You can force them into doing something illegal to get through but you can't stop them from getting through unless you stop everyone from getting through, e.g. by building a very high wall.
There is an interesting developing argument that's been tested a few times, though not in a very prominent way, that features such as this are in breach of the Equality Act (and its predecessors in the Disability Discrimination Acts) for preventing people using assistive cycles from getting through if smaller, narrower cycles can be manoeuvred through the gaps. Here, the feature on the west footway is certainly discriminatory, as it doesn't permit certain types of wheelchair.
These sorts of barriers were installed in many places in London in previous decades, and London Cycling Campaign groups fought many battles in trying to get them removed or reconsidered. I still remember the long campaign that someone I knew ran to get rid of the motorcycle barriers on the River Lea cycling path (often called a towpath, but the old towpath is actually on the other side, and the one on the Middlesex side was built as a 'cycle path'). Ironically, when cycling really took off in the early 2000s, we then had to help Hackney design a better set of barriers around the Hope & Anchor pub (where there hadn't been any before), where thoughtless commuters were speeding through. In one case, a small child was hit and injured, which set the local emotional temperature to boiling point. These barriers are easy to navigate on a bike, including fairly long or wide bikes, and are not at all ideal, but do the job of preventing stupid incidents. It's not an easy balance to achieve where there is conflict like that.
Theoretically, the feature in Trinity Street shouldn't be needed any more, as the further filter outside the Roebuck was installed years ago. This was partly designed to cut out rat-running along Trinity Street, and, probably, Falmouth Road, but motorcyclists constantly drive through it (or so I seem to remember from standing outside the Roebuck). Trinity Street is just too convenient a cut-through.
The locals may still be keen on the present design's speed-reducing qualities, but generally I'd recommend a modal filter design with just well-spaced bollards. It's really not worth bothering with trying to keep out motorcyclists, for the above reasons. Enforcement is difficult, expensive, and risky, and there are actually still very few motorcyclists and motorcycles in London, despite the post-Congestion Charge boom (which is long over but I think may be resuming slightly because of the new delivery firms).
So, in summary, there is no 'self-enforcing' feature that will permit cyclists to get through without dismounting and keep out motorcyclists. As I said, even this one (and one would have to do a bit of observation to get an idea of how people actually behave) probably just causes motorcyclists to use the footway for a short bit. The local residents' association will undoubtedly know more about its history and perceived problems with it.
It's a shit piece of road furniture designed to stop motorcycles using it.
Unfortunately anything designed to prevent motorcycles will also prevent most cycles adapted for the disabled, tandems, cargobikes, or even normal bikes with big panniers.
Is there been a better thought out solution to this @Oliver Schick?