They don't, at least in the USA. My Ph.d. is from Texas at Austin, which is a public institution. During my time as a grad student I had numerous opportunities

They don't, at least in the USA. My Ph.d. is from Texas at Austin, which is a public institution. During my time as a grad student I had numerous opportunities to 'see how the sausage is made'. Even as a public institution the vast majority of funding (over 80% in the sciences) came from outside grants, such as federal agencies. A professors appointment is also only for 8 months of the year, and they must find outside funding sources to cover the other time. This is the business model in each department, and it is why promotion to tenure is so focused on publications and grants.