It seems to me that there was no proper clarification of the order – neither from the paver’s side nor from your side. The surprise about the laying pattern and the existence of the channel indicate this.
we recently had a garden landscaper lay the driveway with granite (10 x 10 cm) in a stretcher bond.
Was this selection your specification or the paver’s suggestion?
At the connection to the street there is a slope, so the stones have to be hewn. In our opinion, the connection looks too restless. Is there a better option?
Yes, of course there are alternatives, but that is a matter of taste. The paver chose a method and consistently executed it uniformly. There is nothing to criticize about that.
We are also wondering whether the drainage channel is needed at all.
That depends on how the property is situated and what the municipality’s requirements are. Building the area without a channel without asking would have been considered shoddy work.
Because the small stone paving with the joints should actually be sufficient to drain the area.
No, the water will run off the area and then infiltrate or drain away there. Many municipalities require that water falling on sealed surfaces of a property must also infiltrate on that property.