1. The campaigns I've been playing in recently usually have 1-2 combats per day. Maybe 3 tops. 4 or more is exceptionally rare. If you have different experiences there then that is fine. I'm sure we all do.
2. Barbarians end up 1 AC behind a fighter.
I guess the Hp thing depends right?
Fight 1 the pure barbarian start with about 6.5 more effective hp. As long as the temp hp gets taken off then both barbarians will have the same effective hp in fight 2. Then a short rest the pure barbarian will have about 6.5 more effective hp assuming hit dice were enough to recover the actual damage taken. In a seriously hard day the False life barbarian will end up with more hp in the later fights as the day progresses because he has more total resources to put toward hp. Draw from that info whatever conclusions you can.
4. Reckless attack is better to use the higher base AC you have and the AC boost still gives respectable AC when using it and great weapon master.
5. The save bonus is the big thing and I think you all are severly undervaluing it.
1. Yes, anecdotes are anecdotes, yours happens to completely support your proposal, which makes it suspect as useful.
2. Um... no? Your barbarian is light on dex, with at most a +1, given they're prioritizing STR, CON, INT, then DEX in that order. Even rolled sets won't get you a +2 DEX. At 7th, you could assume the barbarian has half-plate (15_1=16) vs the fighter's full plate (18). This holds for lower levels as well (and actually favors the fighter for most armor combos). So the +2 reaction use really just puts the barbarian with a +1 DEX and half-plate equal to the fighter.
3. At 3 fights a day, the average fights are much harder, meaning a deeper hp well (14 points deeper while raging) takes on more importance. Further, you're ignoring the argument that this effort takes ALL of the wizard spell slots to reach the near parity in hp available per fight (and that you used four castings and not three for your end of day total, so it's not 4d6+16, it's 3d6+12 or an average of only slightly more total day hp, not many more). So ALL of the supposed flexibility in multi-classing is being used to recover parity on hp alone.
4. I don't see your point, here, as it's obvious that you would suffer less from reckless attack with a higher AC. However, given the barbarian is at a ~16 AC base, bumping that to 18 at 7th, where the average attack bonus is +8, doesn't make much difference in the odds of being hit(shift from ~88% at AC 16 to ~80% at AC 18). It's not that valuable.
5. No, i'm not devaluing it. This is clearly a very strong ability. It's just that the costs for getting it are pretty well balanced (loss of 2 levels primary abilities, delay in ASI, no gain in flexibility due to having to spend wizard abilities to shore up primary class and ability score losses, etc.). It's not strong enough on it's own to make the ability break multiclassing.
i do wish they had made the saving throw bonus equal to INT bonus. Having a +5 vice a +4 isn't huge, but the dip potential drastically reduces to clearly a bad choice.