They weren't initially. They tranformed into modern universities in the 1800s.
'A 1643 publication defined the university's purpose: "to advance learning and perpetuate it to posterity, dreading to leave an illiterate ministry to the churches when our present ministers shall lie in the dust.'
https://en.wikipedia.org/wiki/Harvard_University
Do you think that's what harvard is about today?
> (1) an institution of higher education which (2) offers multiple official, publicly recognized diplomas in secular subjects among others.
A degree mill doesn't a univeristy make. Universities today have to be accredited. Who accredited Bologna? Nothing.
1088 Bologna is not anything anyone around the world considers a university. When people around the world found universities, nobody looks at 1088 Bologna. All modern universities are secular/research based institutions following the humboldtian model.
When harvard decided to transform from a religious institution to a modern university, they didn't look to bologna.