That fuse is absolutely required. Plugs are daisy-chained in a loop with a 32A breaker (The so-called "ring-main").
Removing the fuse will cause lead burn up if there's a short circuit in the device. If you look at the leads on some UK plugs the sizes of the wires can be very small. They can get away with this due to the fuses in the plugs.
My point is that the same thing holds for appliance leads anywhere else. Only difference is in the use of 32A circuit breakers for the rings which then necessitates lower fault impedance to reliably trip the breaker. There is essentially no technical reason why the breaker has so large current rating as in Europe one 16A breaker for all sockets in whole flat typically suffices.
While the article suggests that preferred practice in continental Europe is to have one (typically 16A) breaker per socket, it's not required and usually considered redundant.
Another reason (and probably more relevant) for the fuses in the plug I can see is that when wire that is part of the ring circuit gets broken, the safe current handling capacity of the circuit gets halved and the fuses then offer at least some protection from over-current.
It seems to me that whoever come up with the ring circuit idea understood that it's fundamentally unsafe and thus designed in additional protection measures so the thing at least looks safer.
I'm not familiar with continental Europe's wiring practices, but here in the states, we use 15A and 20A breakers. The maximum number of outlets per circuit depends on what the circuit is servicing. The electrical code has gotten stricter in this area over time. The smallest appliance wiring gauge is typically 18 AWG (about 0.8230mm^2). Given the size of our breakers, I suppose if the 18 AWG cable were overloaded with a constant current greater than 7A, the insulation may melt and cause a fire. I haven't seen it happen personally. I do know (from when I was a kid), that a dead short on an 18 AWG appliance lead will cause the circuit breaker to trip.
Circuit breakers are unsuitable for protecting against long-term (near-)overloads, depending on circuit breaker rating they reliably trip only at overcurrents several times their rated current (with two times the rated current being the lowest and quite rare rating). I've seen three phase 25A circuit breaker catch fire from being run at slight overload for few weeks.
For home/office installations in 230V systems, almost any dead short is enough to trip circuit breaker (and probably several of them in the current path), regardless of wire cross sections involved, as the fault loop impedance will still be small enough to cause >100A of fault current.
Common cords with CEE 7/7 plug on one end and IEC C13 on the other have 0.75mm^2 conductors, which seems to be sufficient for the 10A/70C rating. Two wire lamp cords (and Europlug->C7 cables) are also 0.75m^2. Normal three wire extension cords are 1.0mm^2 or 1.5mm^2 depending on length and (trustworthiness of) manufacturer. Recently, there are also two wire extension cords (CEE 7/17 -> CEE 7/17 "socket" for things like lawnmowers and Europlug -> Europlug socket for who knows what), these usually are 0.75mm^2.
In Czech republic, copper wiring in walls for sockets and lighting tends to be almost universally 1.5mm^2 with 2.5mm^2 used for long runs or industrial installations. It's my understanding that current Czech wiring standards essentially removed any ampacity->crosssection tables and derating factors and only specify allowed resistance of the wire run and it's temperature rise under load. I assume that something similar is also true across rest of the EU.
Removing the fuse will cause lead burn up if there's a short circuit in the device. If you look at the leads on some UK plugs the sizes of the wires can be very small. They can get away with this due to the fuses in the plugs.