If you want to manipulate the meanings and/or the math (unnecessarily), that is your prerogative... but leave me out of it....I've never said you guys can't do it however you prefer.
If it makes it easier for you to understand, by all means stick to what you know. I prefer to define my currents in whatever manner is prudent for me at the time (and thanks for your permission to do so

).
Kirchhoff's current law can be stated both ways (actually 3 ways) and to say otherwise is just nonsense. We could site sources all day that show you are wrong to imply those that do not formulate KCL the way you do are making a mistake, but here are a few:
Slone's Standard Electrical Dictionary (1892):
When a steady current branches, the quantity of electricity arriving by the single wire is equal to the quantity leaving the junction by the branches. The algebraical sum of the intensities of the currents passing towards (or passing from) the junction is equal to zero; Summation(C) = 0 (Daniell.) In the last sentence currents flowing towards the point are considered of one sign and those flowing away from it of the other.
James Clerk Maxwell
An Elementary Treatise On Electricity (1881):
(re-stating Kirchhoff's Condition of 'continuity') At any point of the system the sum of all the currents which flow towards that point is zero.
Kendall L. Su - Georgia Tech
Fundamentals of Circuits, Electronics, and Signal Analysis-1978
Kirchhoff's current law (KCL): The sum of all currents entering any ambit at any instant must be zero.
Carter/Richardson - Univ. of Leeds
Techniques of Circuit Analysis - 1972
Kirchhoff's current law or Kirchhoff's node law, states that the algebraic sum of all the currents entering a junction point (i.e. a node) in a circuit is equal to zero
Handbook for Electricity Metering - EEI
Kirchhoff?s Current Law (KCL) can be stated in three ways:
1. The sum of the currents leaving a junction of conductors is zero at all times.
2. The sum of the currents entering a junction of conductors is zero at all times.
3. The sum of the currents entering a junction of conductors is equal to the sum of the currents leaving the junction of conductors.