As other answers noted, the defence doesn't have to provide evidence at all if they don't want to. It's up to the prosecution to prove guilt in most places, and the defence only needs to provide evidence in as far as they want to challenge the evidence provided by the prosecution.
As for what you actually seem to be getting at:
Having the prosecution take on the entire burden of evidence (of both sides) would be a gigantic conflict of interest that would probably only exist in places you really don't want to live, if it exists at all.
The goal of the prosecution is ... to prosecute. The goal of the defence is to defend. Neither party would be particularly motivated to provide evidence that works against their side. If you want to get rid of this structure and simply have someone provide evidence without the goal to either prosecute or defend, then you'd need to find someone unbiased (and have some way to ensure they're unbiased and they actually do a good job), which could be difficult, to say the least. It's much easier to get 2 biased parties to represent each side.
Separating the two is the best guarantee that each side is represented in the best possible way and that you'd get the most accurate representation of what actually happened*.
Now the prosecution may be, and often is, legally required to share all evidence, and they may have a duty to find all the most relevant evidence in order to be sure of the truth (and certainly should be motivated to be sure they have the right person before charging anyone). But they still wouldn't be motivated to go to the same lengths to find evidence and present it fairly as the defence would (pay someone enough, and they'll scour every inch of the Earth for even the tiniest morsel of evidence that could help your case). The less honorable members of prosecutions may go as far as they can get away with in omitting evidence or presenting it unfairly. The defence is a very core part of the checks-and-balances on the prosecution and a very core part of ensuring a fair trial.
As for why the court doesn't take on much responsibility to gather or test evidence, letting the accused pick their own lawyer to do that is a better idea*. You'd need quite an advanced understanding of the case to challenge evidence properly, so this isn't something that can really just happen within the court. A lawyer (or lawyers), or similar, would need to actually study the case in detail. Having the accused pick this lawyer means they won't be able to argue that the court represented their case poorly (but of course if the lawyer they chose represents them poorly, there may be mechanisms in place to let them choose another). Of course in a lot of places you can get a court-appointed lawyer or public defender, but this is typically provided to those who can't afford their own representation (which is probably a whole other rabbit hole one can go down).
*: (at least in theory)
Let's suppose the prosecution gathers all the evidence. Consider a fairly simple example of an eye witness that would help the defence.
Since the eye witness would hurt their case, the prosecution wouldn't want to mention this eye witness to the defence or court, and they certainly wouldn't want to spend a lot of time or effort actually finding out whether such an eye witness exists, locating them and convincing them to testify.
Assuming they didn't gather their own evidence, neither the defence nor court would have any idea that this eye witness exists.
If the defence gathered their own evidence, they'd be much more motivated to find and present this eye witness.