Until the end of life, no, but at least for a few months / years would be something.
So under the paving stones, lay [Unkrautvlies] on the gravel + joint sand?
I use Neudorff Finalsan Konzentrat Unkraut Frei Plus. You can simply spray it on the weeds and have peace for a few weeks. This means the application is quick and effortless. It is biodegradable, not harmful to bees, and what was important to me, it contains no glyphosate.
Weeds will also grow in the joint sand over time. And if you go over the pavement with the Kärcher to clean it, there is a risk that joint sand and similar materials will not hold.
Poison, of course...
With this joint width, you will ALWAYS have something growing in between, unless it is sealed, which is not allowed.
Re-pave. With very narrow joints. And a drainage channel below with drainage for infiltration, if there is room for it.
Aside from that, I really like it just the way it is right now <3
So under the cobblestones, lay a weed control fabric on the gravel + joint sand?
If you want to do it properly, then the stones actually have to come out, weed control fabric underneath, and the stones put back in. But who bothers for just 3 blades of grass? Even like this, it's not forever.
I also find the burning method okay - once a month is manageable.