Are there any game breaking consequences in this multiclass house rule?

Follow up to this question.

So, as stated in that question, I feel that it is quite weird that a 3rd level paladin + 2nd level Ranger is not equivalent to a 5th level Half-caster (such as a 5th level Paladin), but weaker (being equivalent to a 4th level Paladin).

With that in mind, I intend to use the following multiclassing house-rule for determining the spell slots:

  • Sum the levels of the half-casters first. So, in the example, 3 + 2 = 5.
  • Divide by two. (Divide by three for Arcane Fighter/Rogue – both after summing them together as well).
  • Round it to closest integers, rounding .5 up.

Obviously, this only applies to classes that actually have the spellcasting feature, i.e., the Paladin and Ranger should be at least 2nd level, and the Fighter or Rogue should be at least 3rd level.

Such an idea is not novel and already appears in the Artificer, which is explicitly described as having its half-caster levels being rounded up.

From my understanding, this house-rule will mirror the behavior of single class spellcasting of half-casters and third-casters more closely (not entirely – rounding up would mirror it perfectly). Is there any weird edge case that I am missing that would make this house-rule imbalanced in any way?

The only reason I round to nearest integer rather than directly rounding up is that a 4th level Arcane Fighter would contribute as much to the spellcasting as a 4th level half-caster. Although this is what happens in single class, my gut feeling was that this would make dipping 4 levels in a Fighter, for example, be considerably stronger than before, since specifically 4th level also includes an ASI.