First things first: thank you, Paulo and Michael, for your very kind comments! But don't overdo it, or I won't be able to stop blushing at all ! :-)
Isn't it great? I can answer my own questions! I was reading the coil section of the NVPH specialised catalogue again last night and stumbled upon the reason for the fully perforated Beatrix coil stamps!
It said that from 1984 onwards, businesses handling bulk mail for third parties used special "stamp affixing machines". The reason being that bulk mail tends to get opened more often when franked with proper stamps rather than just some sort of imprint. Those machines had to be fed with coil stamps but in order to let the stamps look as much like ordinary stamps as possible, it was decided to produce coil stamps that were perforated on all four sides!
The majority of the coil stamps made for these machines were commemoratives, but in the early days three Beatrix values were printed: 75c, 90c & 1.40g (all from the original set with black portrait). The latter two values only exist as fully perforated coil stamps, the 75c prepaid the inland letter rate for a while, so this stamp was produced in both types, as these were used very often by the public as well.
So now you (and I) know!