I think one of the big goals of salvaging is to let the player recover particular ships that they really want later in the game, but the problem is that with random drops, in order for the player to reliably get a particular ship, they must be seeing lots of ships every fight. It's also problematic if the player gets big ships too early, both by scaling the player up too quickly and by creating logistics and fleet speed problems for new players. This was (I think) addressed with d-mods so that the player sees lots of ships but they all suck to keep the player from getting strong too quickly, but the player can over-pay to restore the ones they really want which is more valuable in late game.
IMO this has contributed a lot the ship access bloat that I made another thread about. The player just sees so many ships that they naturally progress very quickly towards bigger ships leaving the smaller ones behind. I also think seeing such a large number of bad ships can inadvertently trick the player into bloating their fleet with bad ships and running into logistics problems (since the ships are presented as rewards but are often a net negative to take). It also is just unsatisfying to get offered garbage all the time, getting good ships is fun.
My idea is a new salvaging system:
The player has some salvaging resource which they can use to target specific ships. One implementation idea is that the player can assemble some number of salvaging teams based on their crew size and resources like heavy machinery. The player can choose to assign any number of their salvage teams to any recoverable (i.e. not destroyed) ship after the battle. The chance of recovering the ship and the quality of the recovered ship is based on the the number of salvage teams assigned as well as the size of the ship (and maybe some player skills or something). Also, all the ships they don't target for salvaging give some supplies and fuel, so they can choose to not salvage anything if they just want that.
The idea is that early on, the player will not have enough salvage teams to reliably get cruisers or capitals unless they get super lucky, but they can semi-regularly get one or two frigates of decent quality or maybe a weaker destroyers. As the player gets stronger, they will be able to reliably get more mediocre (in terms of d-mod quality) frigates and destroyers by distributing their salvage teams around, or go for one or two very high quality small ships, or go all in on a single bigger ship with a decent chance of success and lower quality. By late game, they will have enough salvaging capability to reliably get the one really rare ship they want.
I like this idea because it naturally pushes the player towards ships that fit in with their current fleet size and slows down progression a bit (hopefully it could be balanced that way), but still lets the player have a good chance at getting that odyssey they've been hunting for in the late game. It also gives the player more control over what they get, and reduces the number of uninteresting/useless ships the player has to see. It would depend a lot on the balance of the drop rates just like the current system though. It could definitely let the player scale up quickly if they were too high.