I came into this expecting to have to explain that in ARAM there's passive XP gain and move on with my day. Glad I took the time to read it.
You have a great concept, but the problem is this: ARAM is supposed to be a condensed version of a standard match. And because of that you have to have a constant XP gain or else matches on ARAM would take too long or become entirely one sided. With everyone sharing minion XP and kill/assist XP, it'd be nearly impossible to try and keep the levels of players on the map close to even, and harder still to try and keep games from becoming entirely dependent on one or two members of a team gaining levels faster than any other and sweeping. It'd turn ARAM into an early game meta. Champs like Riven, Lee Sin, or Pantheon would take the cake because of how hard they can snowball early. Hence, everyone gets a base amount of XP over time. Keeps the playing field a bit more even by making up for what you're losing in minion XP, and helps even the ones who aren't getting kills and assists keep up a bit.
Still in regards to SR matches you bring up a valid point. When DCd, whether from an internet issue on your part or, more likely, Riot's part, you come back in still at level 1, or at whatever level you were at before DCing. You're essentially just fodder for the enemy at this point. Trying to walk into a lane is like serving yourself up on a silver platter, and a late start as a jungler is nearly impossible in this new jungle from how strong monsters get over time. Most junglers who don't bleed sustain from every orifice are having difficult times with their first clear, and that's with the jungle at its weakest point. But you're still worth 300 gold, and enemies don't care that you were DCd for twenty minutes. They know a level 2 champion doesn't have anything that's going to save you from their level 11 fury.
However, if you try and put passive XP gains in SR you start to find yourself facing a new set of issues. People who aren't actively contributing to the game are now gaining levels as though they were, instead of having to work for your reward through proper CS, smart plays for kills, and sharing assists with teammates. Matches become MUCH faster, and champions who have solo lanes are leveling incredibly quickly because of the combined passive XP gain and all the XP from minions not being split up between them and four others like in ARAM, or like in a standard bottom lane with two players together. To compensate this you would have to cut down the amount of XP given by minions and jungle camps, but that poses it's own set of problems. Cutting the XP given by minions means that bottom lane, or any duo lane, will be permanently behind during the laning phase, and have a hard time catching up afterwards. Jungle camps also wouldn't keep junglers on a healthy leveling curve, as most junglers are aware of what camps they should be at what levels at and use them as benchmarks. Reducing the amount of XP gained passively wouldn't change a whole lot. Reduce it any further than where it is on ARAM matches and you're not gaining it nearly fast enough to do anything. DC for 20 minutes, get back into a match, and in the time most of the other players are hitting level 9 or 10 you might be breaking 4 or 5 from the passive XP. Reducing that instead of minion camps means that you're gaining even less.
You seem to be forgetting that while ARAM has a passive XP gain, you're still gaining levels much quicker than you do on SR because of the minion XP everyone is getting at roughly the same time, and that usually one kill gives four assists. You could take the passive XP gain out of ARAM and people would still level up very quickly because of the mass amounts of kills and assists going on in a short amount of time. This is also why the first few levels in an ARAM match, where everyone is basically just staring at each other angrily, tend to drag on. Once people start hitting 6, the levels start coming in quicker because there are more engagements, more kills, and more assists.
In short, while it's a good idea to give people passive XP, it has a whole slew of issues that really can't be balanced for. The main difference here is that ARAM NEEDS to have a system like that in place because otherwise no one would be getting any XP at all. On Summoner's Rift, it would cause the opposite effect and you'd find people getting too much in one lane and not enough in another.