What zone are you in? Also be careful what time of the year you prune. For instance if this is a desert king and you prune now you won't get any figs this year. Which leads to the question what type of fig is it?

As said by eip3 where is the plant? And wich is the variety?
Branches are too much in number, are thin and too much long.

It is necessary, after a drastic pruning, (and however), to choose few good branches where conduce the growt, cutting back the others.
Action proposed, to reduce dratically in number the new thin branches, and (for my mind) also in lenght; also if for this you loose fruiting.

Owever seems that plant has too much attitude to "go up", in (thin) branches, is the sun enough in summer?.

A question for eip3: why Desert king (in particular) looses the fruiting if pruned? Produces brebas only? Excuse but I do not know Desert King.

A personal question for eip3 (Z7, NY), the plants here lives outside? And: in sunny sites (outside) in your zone have dormant buds damaged by frosts in winter?

Serg, Desert King only produces a breba crop in New York and most of the U.S. except for maybe California due to lack of fig wasp. I am not positive I understand your 2nd question but I only grow desert king in pots because there is die off of the dormant buds if not protected extremely well. Other figs I have in the ground have different amounts of die off and some have very little to no die back. It depends on the particular cultivar.