Quantum mechanics doesn't just have randomness, it has "complementarity" or "the uncertainty principle", according to which two "complementary" properties (the prototype examples are position and momentum) cannot even have definite values at the same time.
The mathematical root of this lies in the properties of waveforms under a Fourier transform - if you squeeze a wave so that it becomes a sharp peak, its Fourier transform will spread out, and vice versa; and the quantum wavefunction used to predict momentum is the Fourier transform of the quantum wavefunction used to predict position. So given the framework of quantum mechanics, you actually cannot get a simultaneous sharp prediction of those two properties.
I mention this because you said you want to understand the philosophy of quantum mechanics with respect to randomness, and the truth is that quantum mechanics is not just random, it is random in this peculiar way such that its predictions don't even involve a classically complete scenario. Instead, in the words of Schrodinger, "at most a well-chosen half of a complete set of variables can be assigned definite numerical values". (But just to be clear, although you cannot get simultaneous sharp predictions for e.g. position and momentum, you can get slightly fuzzy predictions for both, just so long as the combined precision does not violate the uncertainty principle.)
So if you ask, why do physicists believe in fundamental randomness, the core reason is that quantum mechanics is the theory we have, and it works in this certain way. Unlike the usual use of probability, it does not involve a probability distribution over distinct "classical" scenarios. It directly gives probabilities for those "half-scenarios" without offering a glimpse of a deeper reality. So people trying to be true to the theory, treat this uncertainty as something more than just human ignorance.
Now you might say, but maybe there's a better theory in which events are caused. Well, there are such theories, notably Bohmian mechanics, but they all face various problems of consistency with the rest of physics. This is another reason for belief in randomness.
Despite all this, there is chronic dissatisfaction within physics regarding the quantum philosophy. The attempt to make the situation intellectually acceptable produces many different ways of saying "you can't escape the uncertainty principle", some of which do amount to an ignorance interpretation; while other parties seek a completely different "interpretation" of quantum mechanics, such as parallel universes (many worlds).
But because the focus of modern physics is on successful predictions, and the theory works in that regard, one's philosophy with respect to quantum mechanics is essentially regarded as a private matter between you and Nature, almost like the attitude towards religion in pluralistic secular societies.