It is not hellenism.
It is survival.
Reading religious books didn't save a single person during the holocaust.
If it wasn't for army, Jews in Israel would be in the same position as Yazidis - getting murdered and raped by Arabs.
The primary concern is to build a strong army and defend ourselves. Then people can do as much Torah study as they want in their free time.
But without the army, they wouldn't have any time to begin with. We would be ruled, killed or forcibly converted by Arabs.
Reading religious books during the holocaust may or may not have saved Jews, but certainly fighting to the death was the best option.
Now that we're past that deeply offensive statement, allow me to throw it back at you and tell you the reason that Hashem sent us a holocaust according to many of the biggest Ravs of the generation is because intermarriage was at 75%+, because everyone left the yeshiva and was going to school in Germany. The holocaust lost us less Jews than intermarriage, so reading "religious books" may not have saved people while they were being gassed and unable to read, but without them, there wouldn't have been 6 million Jews to kill.
Our army vs. all the Arabs in the world, much more the world world, should have lost every time, and no amount of training could have changed that. There will be a worse holocaust than the last one, too, if Jews continue to proclaim to the world that there is no G-d in Israel.
You can build a gym anywhere. If the government wasn't a traitorous army of secular Torah-haters, we would be building all over Israel, and we would have plenty of room for three times the gyms. If we weren't busy fighting Hamas terrorists who are the sons of Jewish sex slaves, who believe in secular books that say we're all the same, and we need to tear down differences, then there would be more time to train.
They didn't get rid of the Yeshiva to protect the state, they did it to protect the secularism that has been the death of us for over a century. If they need exercise, they can kick out all the Arabs, and will be better trained. The secular ideology says we have to have a people without G-d who fights the Arabs without angering the world. And the statement "no other nation would act like Israel" is patently false, because if the whole world pressured another nation to be suicidal, many would, because the secular political logic is that the allies you will get outweigh the risk of a weak terroristian population. It's irrelevant to Israel, because Hashem wins our wars and turns all the nations of the world against us for our benefit, and if we want to take them alone, we will loose.
Both the army and Torah study in Israel are the foundations of the state, and any reduction in one hurts the other, and without either there would be no state.
Also, better to get raped and murdered by our enemies than to give our women to make children that will do the same to us, and best of all to study Torah and do what it says, and for the moment, it says the army does not belong sitting around in a gym, and certainly not destroying the raison-d'être of the state.