It's partly an issue of keys. Every fediverse actor has a private key and a public key. When my instance sends this to fediverse@lemmy.world, it's signed by my private key, and lemmy.world uses my public key to verify it. When fediverse@lemmy.world sends this comment out, it uses it's own private key to sign it. It can't just re-transmit my comment, because it doesn't have my private key. All it can do is Announce that I've made the comment (and sign the Announce).
Mastodon treats Announces as Boosts, so every post/comment is interpreted as a thing that fediverse@lemmy.world has boosted, so you get all these un-connected posts appearing. I think it's mostly up to Mastodon to remedy.
It works better if a Mastodon actor posts into a Lemmy community, then you get the mix like you imagine. e.g.: https://mastodon.world/@Flash/112095241193510662 (this particular post was crowbarred into Lemmy via !tails, but it would be the same if the author had done it.)