Why don't airports use arresting gears to recover energy from landing passenger planes? An average plane has 50t of mass and a landing speed of approx. 250 (lets be conservative) 200 km/h. Thus its kinetic energy at landing is about 75 MJ or 21 kWh.
The plane catches the wire attached to a pneumatic or hydraulic system, which will decelerate the plane and harvest its kinetic energy. The built up pressure in the system can be released via some kind of turbine to convert the pressure (potential energy) to electricity. Lets say the system has 50% efficiency. Leading to 10kWh harvested energy, per landing.

The airport in Hamburg, Germany is just average. Not large and not small. They had 150 000 flight movements in 2017. Lets say half of them are big planes and 1/2 were landings. That is 37,5k landings per year. Lets say 2/3 could use the arresting gear system: 
This would provide a cumulative 250 MWh of harvested electricity per year. This is equivalent to the electric energy consumption of 100 two person households in Germany.
In Germany 1kWh electricity costs about 30 euro cents (including tax etc). An airport could save 75000 euro per year when harvesting this energy and use it, instead of buying it from the net.
I can't imagine, that such a harvesting system would not pay down after a couple of years.

Why there are no systems like this in the aviation industry?

Con:


You need to refit thousands of planes with a wire catching System
System has to be safe in case of a go-around
???
The energy unit costs for companies in Germany are much lower than for households. Where as a citizen you pay approximately 30 ct / kWh, the airport will pay much less, probably around 15 ct / kWh. 

Adjusting your calculation for this price, we have 37.5 k€ per year in terms of energy cost saving to offset the depreciation and maintenance of the installation. 

Let's assume our bean-counters want to see their investment money back in 10 years (10% depreciation per year), and the yearly maintenance costs are 10% of the initial system price. That means the cost of such an installation at Hamburg airport can be at most 187500.

But mind you, Hamburg has two runways, and each can be used in two directions. To catch 2/3 of the total traffic, we would need to install at least two systems. Runway 23 and runway 15 combined get approximately 75% of the landing traffic, they would be the preferred choice. (traffic percentages per runway are here) 

This brings the maximal cost of a single installation to 95 k€; including project management costs, costs of the equipment, cost of the installation works, cost of closing the runway etc etc. 

That is absolutely nothing! You can't develop and install a system that needs to recouperate 21 kWh in thirty seconds (the duration of the deceleration phase) for such a price. 

And then there is the airborne side of the story. Who is going to pay for the modifications needed on the aircraft, such as an arrestor hook? And for the fuel that it costs to carry this hook around during flight (a hint, it will cost more energy to carry this extra weight around all the time, than that it would harvest at the airport)? And who is paying for the certification of the system?

There is no business case for such a system, not even close.