The ultra rare system in this game needs a serious overhaul asap

The character card system is the worst offender to me. They are nothing more than filler to slow down progression. At the very least, I would like to see the system tweaked so that you can advance your character a rank through prestige once unlocking the initial card. It would be an obnoxious grind, but at least I wouldn't feel like there was a disincentive to use those ultra-rare classes that I may never get to rank X.

Same here.
In ME3 i enjoyed every box i opened. The pool of good characters and great guns was much much larger then the trash once.
Here however i find opening a box instead of exciting me is making me depressed. There is maybe 5 or so guns worth a damn in a pile of 30-40 guns and most of this so called "guns" are not worth even using on bronze let alone in gold.

More and more i just bring the same combo over and over again. Asari Adept whit Talon or Angara Avenger whit Vanquisher. This is boring and annoying. I have attempted to bring different weapons and kits but they are so unrewarding that its a slog. And if there is something i hate is feeling weak and been carried.

Also i dunno if its as common - but the uncommon mods seems to be the ultra rares of the uncommon items. I need 5 more boxes to max my uncommon weapons and have my uncommon characters maxed - yet i only have 3 uncommon mods at rank 1..... And the five or so people on my friends list that i asked have reported the same thing. Is that a bug or just BioWare screwing whit us ?

It seems that the drop priority is weapons > characters > mods. That's why getting the mods is a pain in the ass. 

Since ammo cards no longer have a rarity, wouldn't that mean once someone maxes their rares they'll only pull ultra rares from expert/premium packs?

I do agree with you here and I presume the solution for this issue is some serious balancing. Also 13 weapons + 5 characters are a total of 180 UR cards. In ME3 after all DCLs were out we had a total of 222 UR cards (21 weapons + 3 characters). So the pool is pretty bad indeed.

Having at least a few Level I N7 weapons and characters should be accessible to most or all players (while maxing it to X should require some grind). ME3's style weekend challenges with guaranteed UR giveaways could minimize that accessibility issue.

Nevertheless, the game is just 2 weeks old and the vast majority of players are still doing the campaign and won't touch MP until they are done with that. DAIMP suffered a massive influx of players a month after release with the advent of the weekend challenges. I believe Andromeda will experience the same, therefore I accept the idea that what we have now is an unfinished product that needs some polishing before it starts to shine.

From my experience, I've done unlocking like this;

Buy Basic packs for all common cards (Completed)
Buy Advanced packs for all uncommon cards (Completed)
Start buying Premium packs for Rares and URs (Started on this step. I had spent some money on Premium packs at release (70 boxes worth to be precise), so I have already all rare characters on X, weapons on 5-6 and mods on 3-5)

Drops typically happened in this fashion for me;

Characters -> Weapons -> Mods for both common and uncommon drops.

I did not typically start to see mods untill I had completed all characters at rank X, but even if one out of the three in the pool was completed, it would give me weapons alot more often than it would give me mods. So there is some weighting going on that means it isn't true RNG. 

 There is definetly something going on. Indeed now that i have maxed all my uncommon characters and weapons i started to unlock the mods finally. 

 Funny side note - there is funny rotation going on right now whit my 20k boxes. I would get rare card every second box.... Maybe that will change when i max my uncommon mods but for now its quite good. 

Yes once you get all the "tier" of shit unlocked it does not help with premium packs.

Basically I maxed out all rares, everything and now premium packs just give a bunch of consumables and shit, if anyone was wondering whether maxing out rares results in ultra rares spam from Premium boxes.

There is like 0 incentive to play after you get all rares simply because Premium packs then result in you getting absolute and total trash with a usual chance for URs.

But when it works, it works. I'll give it that.