I'd also love to hear if anyone can frame this in relation to "aid" vs "support" (giving food instead of farming equipment) as well as disaster and colonial capitalism and its long term effects on the actual populace of a country rather than numbers that don't necessarily equate to the lived experiences/quality of life/economic inequality of the populace (like GDP).

I'm going to start with some context about Ethiopia in 1984-85.

In 1974 the Ethiopian Emperor was ousted and in 1975 the then-Ethiopian government, the Derg, or the the Provisional Military Government of Socialist Ethiopia, embraced Communism and embarked on various reforms, including land reform and nationalisation measures. Opposition to the government, both to particular reforms and to general government mismanagement and corruption drove a civil war in Ethiopia from 1974 to 1991.

So the context of Ethiopia was famine relief being delivered to a country in the middle of a violent civil war, with the official (Marxist) government of the day having control over only parts of the country - but those parts included the ports.

I'm going to discuss two aspects of the impact of Live Aid, firstly on the health of the people and secondly on aid practices.

There's not many studies on the impact of the aid itself on Ethiopian people, the only one I'm aware of is Dercon, Stefan & Porter, Catherine. (2012)., Live aid revisited: Long-term impacts of the 1984 Ethiopian famine on children. Journal of the European Economic Association. 12. 10.1111/jeea.12088. This study looked at the height of adults who were infants during the famine, relative to their siblings who were either older or younger, and found that they were significantly shorter as adults, and couldn't find signs of relief operations at the time making a difference. The article says it's the first study of the impact of the famine on outcomes. That said, this study doesn't tell us anything about the children who didn't survive the famine. I can't find any studies that look at the impact of Live Aid in terms of lives saved, I expect the civil war made it hard to collect data, at times the British Air Force was dropping relief food from the air. And it wasn't like it was back to normal once the famine was over, the civil war kept going for years afterwards. In those circumstances, determining the numbers of dead is hard, let alone the impact of a particular intervention. The other aspect I want to discuss is the impact of Live Aid on aid policy. The Live Aid relief effort was criticised by Spin in 1986 for funds being diverted by the Ethiopian government of the day to buy weapons to win the civil war and continue its (much-hated) resettlement policy. See Spin retrospective in 2015 on their 1986 report. However in 2010 the BBC apologised for a report it had made earlier in 2010 along those lines, after an internal investigation had found said claims unsupported. In summary I think we can say that Live Aid's high profile raised awareness of the risks of humanitarian aid in countries with abusive governments (and quasi-governments).

More generally, there's an ongoing economic debate about the effectiveness of aid (all aid, not just Live Aid) in reducing poverty. A criticism is that a government that gets most of its revenue from the economic activity of the people that it governs has incentives to be more responsive to said people's interests than a government that gets its revenue from elsewhere, be that natural resources or foreign aid. Here's an accessible summary of the arguments. Note that this argument is based on data across numerous countries and does not relate specifically to aid to Ethiopia.

In summary, the benefits of Live Aid are doubtful, but there's been basically only one study on it. The one study found no effect but couldn't include raw lives saved. Talk of Live Aid funds being diverted to continue the civil war and severe human rights abuses seems doubtful, but there are general concerns about the effectiveness of foreign aid.