The main issue is cost. I work in HR at a major organisation and I've read through some of the internal reporting on graduate programs and other student initiatives and they represent a massive cost to the business. The expense that goes into recruiting and training graduates/students added to the fact that they are often limited in what they can do reduces its viability for many organisations. Investing money into graduates/students is something which only pays off long term if the students progress to managers/leaders within the organisation. But if they leave after spending only a few years with the company, then the organisation pretty much loses out on its investment. So it's really a big risk, which is why these programs are rare. All of this stuff adds up to a super competitive graduate/student market.
I'm speculating here, but the Big 4 mainly do it because they can afford it and a large part of their business model is based on developing talent from the ground up.