Very little "breaks," in 5e but I don't think this DM has really thought this houserule through very well.
As a threshhold issue, this ruling greatly privileges multiclassing over singleclassing. Especially those who multiclass multiple times (more than dual-class; in other words, there is no real detriment to "dipping" in many classes).
I rogue with a 2d6 back stab at level 12 instead of 6d6 .... sure their is no loss there.
A fighter with 2 attacks instead of 3 attacks per action at level 12 .... sure their is no loss there.
A wizard that cast higher than 2nd level spells even thought they have 6 level spell slots .... sure their is no loss there.
Its almost if your bias against multi-classing an don't see how the lose of class abilities, known spells, and lack of the typically stronger higher level and capstone abilities as significate enough a trade to pay off the gains from low level dips... I wonder if you made a 4/4/4/4/4 character (get all 5 feats anyway, max 3rd level spells) and I hand an full caster with 20 levels a 9th level spells who would win in a battle royal? I like my odds.
If your a max/miner your never going to be a full caster and take more than 3 of a second class and lose any chance at the most powerful spells in the game. If your primarily a rogue every level is a lose to your main source of DPR, If your a tank Barbarian your taking smaller hit dies which is likely a huge lose to your HP, if your a monk your losing dice improvements for melee and monk weapon attacks as well as speed....
Really the only class that gets to multi-class with abandon and gain more than they lose for multi-classing every class... is Warlock. Your typical smite knight (warlock/paladin) will still be around but I would point out the any build really worth muli-classing to any extreme or more than once would be as common or uncommon as they are now as you can already get ASI and feats every 4 levels of each class and 4 one level buy is only a lose of 1 feat for multiple first level abilities.
I personally think if you want to delay all your good abilities and mix all the classes together … can actually get it to functionally work.. and manage not to step on anyones toes....then It doesn't matter if you get all the feats or not. More than likely it would be a build that looks great up front but you find when the other classes are getting late game abilities your going to be a "jack of all trades but master of none" and largely underpowered and underwhelming. Their maybe an exception or two but not many.
As far as Fighters feats, you just make them class specific for lvl 6 & 14. Done. Easy.
