Would a unified global government further humanity or hinder its progress?

There are types of government that could do either, depending on how you define "progress". It would be possible to have a global government if there were enough technological advances that allowed administration of all parts of the globe to come from a single entity. Managing that government would be a huge undertaking and it would take a great deal of buy-in from the individual areas on the rest of the planet.

IMO, a successful global government would look more like the original U.S. Constitutional Federal-State system, where we are all a loose confederation of states with different programs, statutes, and cultural norms, and a larger mostly hands-off Federal government that can settle disputes, provide baseline policies, and provide regulations for inter-state commerce and population movements. The UN is a radically different and much much weaker global body than this, and I don't think any global Federal system would succeed simply by using a "stronger" UN as the model.

One factor to consider is when there are other areas of the universe that have human colonization. Having governments on a per-planet or even per-solar-system basis would help a lot towards that effort.

The biggest problem you're going to have is how different religions want to disenfranchise and kill one another. But once we get past that, it should be a breeze.

Hinder. While the people of the globe should be unified through individuality and voluntarism, centralizing government to that extreme is binding and dangerous. It takes only one generation for a government to go from the best of intentions to the worst of intentions. Globalizing that government can result in one of the greatest disasters humanity has ever seen.

Hinder. I don't usually quote the bible, but the the phrase iron cuts (sharpens) iron is real. If you think about it, struggles actually cause innovation. In Tibet, the buddhists have sanctioned debates on purpose to stimulate that creative energy. A sole unification should only happen at the level where things may be dangerous to humanity as a whole.

That's tough to say for sure, in all likelihood it would hinder it. However, if we had one main government whose sole job was to make this world a better place, not for the wealthy, but for everyone, I'd like to think it would make life better, especially for all those people living in third world nations suffering needlessly under dictatorships. We come from different cultures and speak different languages, but we're all human, we're not as different as we think we are. Unfortunately it's highly unlikely this would ever happen since we're so divided in our thinking and laws.

Throughout history, most governments have hindered mankind's progress, being concerned only with perpetuating and enhancing their own power.

It would bring the global population down to the lowest denominator .

Imagine Haiti or Honduras on a global scale .

Power must be shared between local administrators and national/global ones.

United we stand. Together we fall.

Fall with me America

- Donald Trump 2016

It would greatly hinder it . It will make everybody a slave to the elite heads of government .