It's often been quite unclear to me (and I dare say to a lot of people) what precisely the allegation was - whether it was that Hunter Biden had personally been involved in Burisma corruption and his father helped cover that up, or that Hunter hadn't been personally involved but had persuaded his father to shield Burisma from investigation/prosecution for its earlier corruption, as a part of his job as extremely well-paid BoD member of Burisma. So now you made clear it's the latter.
I think the main reason why I understood it differently, is that this latter case would, surely, require much more investigation in the US than in Ukraine? I mean, if you just want to prove Zlochevsky/Burisma's original corruption prior to 2014, isn't everybody just taking that for granted? The key point in this case, as far as I can see, would be to show evidence of Joe Biden personally setting US policy or taking decisions that improperly favoured Burisma - more on that below. How are you going to find proof for that in Ukraine, or why would you expect the Ukrainians to provide it? Yeah, they saw Joe Biden visiting and making the now-infamous threats about Shokin, but how would they know to which extent that was Joe Biden's own idea?
Article on the EU's criticisms about Shokin, Nov 2015: http://www.ukrweekly.com/uwwp/new-round-of-western-criticism-targets-procurator-general-shokin/
Article about the EU's reaction to Shokin's ouster, March 2016: https://www.irishtimes.com/news/world/europe/eu-hails-sacking-of-ukraine-s-prosecutor-viktor-shokin-1.2591190
Article on the IMF's position (it doesn't seem like Lagarde mentioned Shokin by name precisely, but it was implied), Feb 2016:
https://www.ft.com/content/44c1641e-cff7-11e5-831d-09f7778e7377
European Parliament briefing on Ukraine, July 2017, which (among many other articles along the same lines from 2017) makes clear that indeed, after Shokin got fired, Lutsenko didn't necessarily impress the EU any more:
https://www.europarl.europa.eu/RegData/etudes/BRIE/2017/608632/EPRS_BRI(2017)608632_EN.pdf
European Council on Foreign Relations briefing on Ukraine, August 2019, heavily criticizing both Shokin and Lutsenko and providing wider context on the EU's views on Ukraine and specifically it's prosecutor's office: https://www.ecfr.eu/publications/summary/guarding_the_guardians_ukraine_security_and_judicial_reforms_under_zelensky
I can find a lot more if you want, this isn't exactly obscure stuff. Certainly, the EU wasn't impressed by Lutsenko any more than by Shokin, it wasn't necessarily an improvement. But although they could and did push Poroshenko to fire manifestly unsuitable or shady people, they couldn't decide who the replacement was going to be.
So when the US ambassador to Ukraine went and openly called out the Ukrainian government for its failure to properly investigate Zlochevsky (https://m.facebook.com/usdos.ukraine/posts/10153248488506936) in September 2015, is that supposed to have been some rogue move going against the Bidens' great conspiracy? Hint: no, it was quite in line with the policy of both the EU and the US to keep pushing for investigation of corruption in Ukraine, in general but certainly including Zlochevsky/Burisma, and pushing to oust Shokin because they felt he was not only not getting the job done but even sabotaging it. Threats of withholding funds were made, sure, not only by Biden but also by Lagarde of the IMF, and I think I saw somewhere the EU did it as well. But they had good reasons to make those threats and they were executing their country/organization's policy, not pursuing personal goals. It's just not credible at all that in that wider context, Biden could have decided by himself whether Shokin had to stay or go, or more generally could have taken steps to shield Burisma, without red flags going up all over the place.