I still do not understand all the criticism about "per"
If I drink one glass of water per hour, I am not saying that I drink one glass of water divided by an hour. "per" is an English word with many definitions. All language cannot be converted into math formulas.
I believe that you are getting lots of criticism because you are using 'per hour' in a technical setting in a way that is different from its technical meaning.
Language is not dead, 'per' has more meanings then its technical meaning, and not everything can be expressed in equations. However when 'per' is used with units of measure, it has a _specific_ technical meaning, so any casual usage that doesn't fit the technical meaning is going to stick out like a sore thumb.
When you express rates, you always take <quantity> divided by <time>.
Most of the rate units that we deal with don't have special names, instead we say explicitly 'quantity unit per time unit', for example miles per hour, gallons per minute, meters per second, etc. This usage is the specific technical meaning of 'per'.
A few rate units have specific names, and for historic reasons many electrical units are actually rate units. Amp, watt, lumen, curie, etc. are all rate units. The unit itself already includes the concept of some <quantity> per <unit time>. An amp already includes the concept of some number of electrons per second, a watt already includes the concept of so much work done per second, a lumen includes the concept of so many visible photons per second, and the curie so many radioactive decays per second.
Perhaps it would be simpler if we didn't give these units special names, and instead said 'coulombs per second' for amps, 'joules per second' instead of watts, or 'becquerels per second' rather than curies...but we are stuck with the historic fact of these 'rate units'.
I get that you are using 'amps per hour' in a casual sense to convey a quantity. But this usage really is a problem because you are using something that has a specific and known technical meaning in a casual fashion that distorts that specific technical meaning.
The correct way to take a rate unit and get back to a quantity is to multiply. In this way you have divided by a time unit and then multiplied by a time unit, to get back to a simple quantity unit. 1 'amp hour' is a quantity unit, meaning 3600 coulombs.
When you divide twice by time, you have an acceleration unit. Miles per hour per hour doesn't say how far you go; it says how quickly you are changing speed. Because amps are already rate units, and already include the concept of <quantity> /<time>, 'amps per hour' is an acceleration unit.
Imagine that we had a named rate unit for speed. Heck, lets make one up, and define a 'cugnot' to be a speed of 1 mile per hour. So instead of saying '60 miles per hour', we could say '60 cugnots'. With this rate unit defined, a cugnot hour is one mile, and cugnots per hour is a measure of acceleration, equal to about 1.47 feet per second per second, or about 0.046 G.
I also stated that we use the word amp by itself. The per hour is not stated, it is understood.
I still do not see the problem if someone from the basic electricity class takes a physics class.
Only that by saying amps per hour you are confusing a rate unit with a quantity unit, leading to something that will need to be unlearned later.
-Jon