Litvishe, kollel students are not exempt from military service; less still are they allowed to “exempt themselves.” Instead, they are deferred on the specific grounds of their studies. Leaving kollel for any purpose (not only to go to work) revokes the deferral. The same applies to small numbers of university students who are allowed to earn degrees in specialized fields provided they sign on for extra years of army service afterward.
You speak of “secular university students” but the university system doesn’t distinguish between secular and other. Students don’t get cash in hand from the government, although universities do give stipends to a small number of selected postgraduates. What does exist for universities is massive government funding, without which tuition might be twice as high as it is. Those who can’t gain admission to universities go to colleges, which get no subsidies of that kind and charge whatever their prestige and track record allow them to.
Comparisons of kollel with university are mostly apples vs. oranges, and since in Israel both systems vie for a piece of the same pie, it’s almost structurally inevitable that each would accuse the other of leeching…