Given the way it was phrased/proposed, it was rather clearly a proposal that was meant to be rejected, but made in order to generate news like this. (Would Russia accept a UN investigation about Bucha? The answer is no. Or about the Olenivka prison fire/explosion? No again. Likewise China is supportive of this Russian proposal, but does it want anything in Xinjiang investigated by the UN? Again, no.)
So that would be the main advantage of the proposal. On the snowball chance [in hell] that it would be adopted like that, it would have advantages [for Russia/China] of repeating the same accusations at multiple sessions etc. And if the Western countries were foolish/pressured enough to accept, they'd have expose their own investigative methods about submarine events in order to cooperate, their armed forces precise movements, etc.
The Russian proposal roughly coincided (within a few days) with the one-year anniversary of their invasion. That, of course, made it even more easy by the West to dismiss it as a distraction tactic.
Regarding that "proof" see https://skeptics.stackexchange.com/questions/54372/did-the-cia-blow-up-the-nordstream-1-pipeline-using-baltops-22-as-cover
BTW, I'm not sure UN has ever investigated explosions. A quick search found that there were calls for an UN investigations into the 2020 Beirut explosion, but I'm not sure that went anywhere either, even though no big country seems to have a reason to block that.
OTOH, in the 1970s, the UN secretary general was granted [standing] extraordinary powers to investigate chemical attacks (seemingly granted around/after the Vietnam war), authority which was [much] later used in Syria. But more recently , Russia tried to have that authority put back under UNSC aegis, which Western countries allege was so proposed in order for Russia to control/veto the outcomes of such investigations.
By the way, the Russians or at least the Russia-related companies did conduct their on-site investigation[s]. When some Western journalists went to look at the site themselves, they could also see a (larger) Russian ship (the Nefrit) in the area. And it had been there probably for two weeks prior, given when it was first spotted.
At least for Nord Seam 1, Nordstream AG which is 51% owned by a subsidiary of Gazprom, did put out the result of their on investigation, which was roughly limited to observing the "technogenic" nature of the seabed craters and their dimensions/locations, and the spread of fragments around those.
So the issue is not so much agreeing what happened but "who'd done it". And proving the latter requires access to mountains of data that countries do not typically turn over to the UN. So, the "advantage" of agreeing to that in this case would be setting the standard/precedent that Germany, Denmark, and Sweden are presumed more corrupt and/or incompetent than Lebanon in such matters.
Speaking of Lebanon, there was a UNSC resolution (1757) [over a decade ago] that did authorize an international "Special Tribunal for Lebanon" to look into the death of PM Rafiq Hariri, who died in a blast. After over a decade of investigating, the Tribunal did try some Hezbollah members in absentia, because the latter would not cooperate. And the Tribunal convicted one person, who is still at large (Hezbollah did not surrender any of the suspects). The Tribunal also failed to connect that operative with explicit orders from any higher-level players. So that's probably the most you could expect an UN investigation to pull off in a case like this.