Why is it advantageous to have most of this done by the node itself rather than independent chain explorer and analytics type tools, similar to what you get on blockchain.info?

IMO, if it can be done outside the node, it should be done outside the node. The node itself being critical to the functioning of the network. What if a bug is introduced that introduces a crash of every node on the network when some statistics counter overflows? I'm not saying this is likely, but the risk is entirely unnecessary.

Obviously per-node mempool data needs to be collected by each node, but I don't really see the network as even remotely large enough for that to matter. Bitcoin only reached that point recently.