I think there's two separate questions here:
First one: should the current level of need for homelessness charities and food banks exist? Absolutely not - the state should be preventing the levels of poverty and homelessness by addressing the systemic causes and righting the failures of government policy that cause it.
Second one: should charities have a role in addressing need, or should this wholly be the responsibility of government? I think it's really important we have a strong civil society and don't rely entirely on the state.
I generally believe in a big, interventionist state - I think those with broader shoulders should pay more tax to support those with greatest need. But I completely agree with the arguments @TempestTost has made above more clearly than I can articulate.
Basically, putting all your eggs in one basket called 'state support' isn't good for society.
Charities can be responsive to local need - both in speed and in actually understanding exactly what the need is and meeting it.
Charities can do things that meet need but wouldn't align perfectly with government policy, so the government simply wouldn't do it. A state-run food bank doesn't really make sense.
Charities can more trusted by those in need - it's hard to get away from the power imbalance issues with state-run service (you can't really get away from the fact that at the extreme end of things the state has the power to deprive you of your liberty). Think about charities working with refugees with no legal status.
Charities are an 'insurance policy' against the state - you can't rely on the state always being there and in the best interests of those in need (I know people who work in homelessness charities in the USA and they are despondent about what they think is going to happen in the next four years, but thank god they exist!)
Charities can speak truth to power and mobilise communities to speak up against injustice. They can bring about change to government policy.
Charities can provide people with access to justice and challenge the state though the legal system (look at law centres or the legal work organisations like Shelter do)
Yes - it's imperfect. Small charities can be poorly run or in some cases do more harm than good. Large charities can get too close to government or too invested in perpetuating their own dominance. But in an imperfect world they are vital.