Severus Snape and Memory Charms
So firstly any evidence collected by Dumbledore via Harry's memory is not going to convince Fudge, the Ministry, or the wider wizarding world. Those that believe Dumbledore/harry don't need it, and those that don't won't believe it. We know Fudge et al wouldn't buy it, because Fudge is paranoid (to the point of harming his own cause) about Dumbledore wanting to take his job. So why wouldn't the rest of the Ministry/normal wizards not believe?
Because the wider wizarding world, those that didn't believe Dumbledore/Harry in the books, would not have been swayed because Dumbledore is the Greatest Wizard of the Age. All Fudge/the Ministry would have to do is go "Of COURSE it looks like a real memory, Dumbledore did the Memory Charm!" Or "Of COURSE Harry can accurately describe the dark magic, Dumbledore told him/modified his memory such that he can give accurate descriptions!" Then everyone nods knowingly and, very proud that they've seen through Dumbledore's underhanded scheme, goes on with their day.
So the only real question is why Dumbledore didn't get Harry's memory for his own intelligence. The reason is that he has Snape. Yes I know Snape wasn't there, bear with me. Dumbledore believes Harry, and trusts Harry to tell him the truth as accurately as possible. Yet even so, there's a limit to what Harry can tell him with regards to hand gestures or minutiae of incantations. Heck, even the memory may not show clearly the details required. BUT Dumbledore has Snape, who he also trusts unreservedly. Snape arrives two hours after the event, and is taken back into the Death Eaters. He has the PERFECT cover to ask a load of questions to everyone surrounding the events of Voldemort's reincarnation about the details of said reincarnation. Indeed, if he's supposed to be a fanatical adherent it would probably come off as pretty weird if he didn't try to get every "glorious detail" of his Lord's return.
Between Harry's recollection and Snape's intelligence gathering Dumbledore likely felt there was nothing more to gain from re-examining the matter via a memory of the events, especially if Harry and Snape's stories corroborate each other.
Conversely, Dumbledore could have been worried about false intelligence from re-living the memory via pensive. Harry's recitation of events could be true in broad strokes, but Voldemort is a skilled and subtle wizard. Maybe Harry's memory of the event would show some piece of intelligence too subtle for Harry to have realized its importance, yes. But that subtlety could itself be a trap. We know Dumbledore (and indeed anyone) could tell that Slughorn's memory-mod was a shoddy job concealing something. But we have no idea what a high-grade version would look like. Perhaps Voldemort was capable of creating seamless modifications? Or the smaller the "edit" the harder to catch. It seems within the realm of possibility anyway.
So why couldn't Snape be used to sort out these subtleties as well? Snape can ask general questions about Voldemort's revival, but pointed questions about specific details are always tricky for spies. For example, let's say that Voldemort HAD modified Harry's memory a bit, to show Voldemort wearing a purple ring during the reincarnation process. (Yes that seems like an obvious thing but I can't think of something truly subtle atm) Harry doesn't mention it because he's essentially Muggle-born and doesn't think it's worth it. So Dumbledore uses the Pensieve to re-watch the moment and sees the ring. Seems important to him. Voldemort is very talented, Dumbledore doesn't catch the memory mod. So Snape comes back, tells what he learned. Dumbledore asks about the ring. Snape's sources didn't mention a ring, but he also wasn't asking specific questions about what Voldemort was wearing as accessories. Snape goes back and brings up jewellery in his next conversation with Voldy/a Death Eater. Snape is caught as a spy and executed, because Voldemort knows the detail is only something Dumbledore would notice while watching the modified memory. Or Snape is used as a double-blind and is told some mumbo-jumbo about it being Real Important, which he then tells Dumbledore and wastes Dumbledore's time. Spying ain't easy, and it's much safer to ask "tell me what happened, spare no detail!" than "hey did this One Explicit Detail occur?"
Or it's not something that can be easily double-checked by Snape, like a certain hand gesture even an attentive Death Eater might have missed. Then Dumbledore has no way of verifying whether it was true or false. Which makes the intelligence suspect. So why waste time gathering problematic intel, when there is good and corroborated intel? Sometimes it's better to only have half the story but that half be 100% right than 100% of the story but have no way of knowing what's true or not.
TL/DR
Anything Dumbledore finds can't be used to convince people, because Dumbledore's rep as a powerful wizard would let Fudge easily play it off as a lie. Anything Dumbledore could have found out in the memory for his own gain could be more accurately obtained/corroborated via Snape, or would be of suspect veracity because of the potential for memory modification.