DND_Reborn
The High Aldwin
Sure, but it would be compared to a 10th level fighter in output, and that's a very different comparison. You wanted to know why the rogue did so much damage? It's a 10th level character.
Except he is being compared to other "10th level" characters, i.e. the Fighter/Barbarian 5/5 and Barbarian/Monk 5/5.
What you're going to see, very soon if not already, is that the basic math of the game breaks down when you're freeing stacking 20 levels (or 30, in your case) of character abilities and synergies at "10th" level. You've made a change that undermines a core mechanic of the game -- it will break. Maybe you'll do fine with it, but your rogue is going to continue being a combat beast because they'll reliably get the 'one big' rogue hit and follow through with full fighter damage output. At 11th level, the assassin rogue will be making 4 attacks a round for 7d6 (sneak)+4d6 (4 weapon)+20 (assuming 20 dex) = 59 damage average. The regular fighter/barbarian will be doing 3d8 (longsword)+15(stat)+12(raging) = 41. It's not really close at all, because you've broken a core mechanic of the game. In the assassing crits (and I'm assuming they've gone champion?) or gets an assassinate round? Phish. In martial classes, being able to stack that free sneak attack hit onto a fighter attack routine is tremendous. There isn't an answer for it in the other martial abilities (at least with the choices you've made, a fighter/barb great weapon fighter with the right feats and your multiclassing rule would dish serious damage and almost never miss).
Your multiclassing rule will supercharge your martials and not do much at all for your casters. The reason is that martial abilities tend to stack and not consume more of the action economy while the casting classes can still only cast 1 spell a round (mostly, there's some sorcerer cheese you can pair with other classes to do some very interesting things, sorc/warlock under your multiclassing is a beast).
Heck, just spitballing, but a paladin/warlock/barbarian would be ungodly. Like, badly so. Greatweapon raging smites with GWM/GWF, PAM, Reckless Attack, and warlock slots while wearing platemail and taking 1/2 damage from everything? Maybe warlock isn't the right call, though -- sorcerer would be strong as well for the slots and the ability to close out a super nasty attack routine with a quickened twinned debuff/buff or a quickened fireball. Yeah, your M/C rule is straight out broken.
Honestly, I don't remember what archetype the rogue/fighter went for the fighter class, but I believe it was Cavalier (I know he didn't take Champion). I could be wrong, I would have to ask the player. I know the Fighter/Barb went Champion/Totem Warrior and I think the Barb/Monk is Zealot/Shadows for archetypes. The Sorc/Druid went Dragon bloodline/Moon I am pretty sure. For my triple-class I chose Scout/Knowledge Domain/War Magic. I find my spellcaster is doing very well and having so many slots available allows me to not have to toss cantrips most rounds.
Regardless, if our system works for us to meet the challenges we face and the play style we like and our DM fosters, it isn't broken.

It might not be to your liking, which is fine, but we like having more options and features, and so far it has worked very well, thank you. Now, as I have stated repeatedly, the only issue with the rogue doing so much damage was because the DM was misusing assassinate by allowing it nearly every encounter. With that remedied, our last session went much better in that respect anyway.
