The technobabble is that all TN ships operate in the Aether, regardless of whether they are moving. Wrecks have lost integrity so cannot remain in the Aether. If you don't accept that as reasonable, that's fine, but the lore is there to provide some rationale for the game mechanics, not vice versa. It's also not logical that ships in Aurora function like ships in the sea, but the gameplay is better with that paradigm, so the Aether exists to provide a rationale.
You used to have to find wrecks, but it was tedious so they became visible in later versions. At the time, everyone agreed with the change.
I'm not adding tugging wrecks because it makes recovery too easy, especially for wrecks in contested system, claimed systems or in orbit of NPR home worlds. Sneaking in to salvage key wrecks creates some fun situations.
I don't think stabilization is a no-brainer. For example, Invaders don't have jump drives. It also makes them easy to detect. I have several jump points in my current campaign that I won't stabilise, for both those reasons.