Let's get this out of the way: I don't like the equipment progression in Mass Effect: Andromeda. It's a whole lot of busy work that has me spending too much time flipping through menus and worrying if I have enough beryllium. That said, complaining about the specific way the latest AAA RPG screwed up crafting isn't particularly novel or interesting.
So here's how I'd do it.
My main design goals for this are:
1: Allow the player to experiment with different equipment choices while allowing a sense of progression as they go through the game.
2: Emphasize the role of the Andromeda Initiative where ever possible. The Pathfinder doesn't do everything themselves, after all, they merely clear the way.
3: Make sure the player isn't worrying about the exact numbers or combing the world looking for something in particular too often.
My main inspiration for this is RTS building trees, except replace the different units and upgrades with weapons, armor and modifications.
Basically, the core loop is that the Pathfinder finds sites for the outposts to collect resources and research new tech. Instead of the current system, where you deploy probes, mine mineral nodes, and scan everything in sight, the Pathfinder investigates potential building sites on a somewhat larger scale. For example, in the current game, where there is now a mineral site, the pathfinder finds some problem preventing the Initiative from harvesting in that location, solves the issue, and moves on, unlocking the main outpost to expand into that location and harvest the resources. You could make this as much of a narrative beat as you want - something as simple as clearing out a Kett patrol or as complex as a lengthy, planet-spanning quest.
You can expand this out to a lot of other areas as well, although scope would be an issue. Limiting ourselves to what's already in the game, distinct Remnant sites and mineral locations would take the place of the current research points and materials and increase the viability of the colony, allowing the main outposts to use the Andromeda Viability Points or something similar to create facilities to develop new weapons, armor, and modifications. You could have different materials and research types required to develop the different tech categories (milky way, andromeda, remnant), but instead of unlocking individual weapons for development, I would go by rarity - unlocking all the common items first, then upgrading the buildings to unlock the rare and ultra rare items. (Incidentally, I don't think the inventory or equipment tiering add anything to the system, so they can go too. Tiering would likely be pretty simple to plug in, though.)
I particularly like how this system might represent the idea of a growing and developing colony, something that the current game significantly lacks, as far as I've seen. A place might start out wild and dangerous, but as the pathfinder moves through and solves problems, people move in and start making it a home. I also think it would be a great way to characterize each individual planet in a fashion I've not seen - lots of little problems dealing with the peculiarities of the planet, instead of just "once we clear out the radiation this planet will be viable for our colony." It also bypasses the invisible perks on the Nexus, where I don't think it makes sense for the pathfinder to have much authority anyway, and focuses on the ground colonies and how they develop over time.
Something that would require some more work is the details of how the main outposts function in the system - consideration should especially be made for developing the assets to represent these buildings. My current thought is marked off plots, with certain types of buildings (or building trees) able to be built in specific locations, allowing a unique, identifiable character to be attributed to individual outposts while still allowing a fair amount of customization.
You could also extrapolate this out to add a lot of other systems - food, housing, defense, etc etc (like a less freeform Fallout 4), but would quickly explode to the point where it detracts from the other aspects of the game. That said, I think this system as I've outlined here would do a lot to eliminate many of the frustrations I've had with Mass Effect: Andromeda and better represent its thematic and narrative ideas.
P.S. This idea as laid out would admittedly require quite a bit of art and other assets, which are time-consuming (and thus expensive) for a development team. I believe you could make a version of it minimizing that aspect without compromising functionality - basically just having it work similarly, behind the scenes, without a visible representation in the world. That said, this being tied to one of the main thematic beats of Andromeda, I personally think it would be worth the investment.
P.P.S. Thus far I've only explored most of Eos, but given the way it's been set up so far I feel confident that at least this aspect of the game isn't going to get much better.