Use of breve
The breve is only used for emphasis.
In the typical Latin text no breve or macron appears.
When vowel lengths need to be indicated, it is often done by adding macrons over all long vowels or only those that are useful for clarity.
It is only when extra care is needed that the length of every vowel is indicated, and this is where the breve comes in.
I don't think I have ever seen this approach taken in a full sentence, but only in grammars (usually only when discussing morphology) and some dictionaries.
Even in many dictionaries only the long vowels are marked and the absence of a macron indicates a short vowel.
This is logically enough, but sometimes redundancy leads to better communication.
In the absence of any markings one can always ask whether a vowel is long or short, but no ambiguity remains if a breve or a macron is present.
Sometimes people use individual breves for disambiguation.
For example, pŏpulus is "people" instead of "poplar" and băro is "baron" instead of "idiot".
Macrons can be used similarly when needed.
In Lewis and Short the breve has a special disambiguating function even though macrons are used.
Both ĭ and ī are vowels, but the unmarked i is a consonant.
This is a reasonable convention, as it makes the pronunciation clear and does not resort to using j which is a less common spelling variant even for consonantal i.
When precision is needed, consider also the disambiguation between I/J and U/V.
Breaking diphthongs
There is a third diacritic, the diaeresis.
It indicates that a vowel belongs to a different syllable than the preceding one but makes no comment on the length: aëris (from aer) has three syllables but aeris (from aes) has two.
Sometimes they are added to assist people less fluent in Latin, as in the name Nausicaä; two consequent a's are always in different syllables in Latin, but that is not obvious to everyone.
The diaeresis is a common way to mark broken diphthongs.
If either vowel has a macron or a breve, then the two vowels are understood to be in different syllables instead of forming a diphthong.
If you want to indicate that you have a diphthong, you can spell ae with the ligature æ instead.
This ligature is only used for the diphthong.
This option is only available for ae and oe, but disambiguation is rarely if ever needed with the other diphthongs.
(In some cases you can indicate a diphthong by drawing an arc over the two letters, but I have only found that useful for singing instructions when the singer needs to be reminded of the diphthong.)
Vowel vs. syllable quantity
Sometimes macrons and breves are used to indicate syllable quantity instead of vowel quantity.
This is particularly common in poetry where syllable quantity is what matters.
No convention is universal, so your readers are likely to be slightly unsure what you mean by diacritics unless you specify it explicitly.
Conclusion
The whole point of diacritical marks is to communicate more effectively.
There are no hard rules as to when and how they should be used, and the best choice depends on context and goals.
In typical texts no diacritical marks are used at all, apart from perhaps the occasional aëris, pŏpulus, and senatūs for clarity.
What you describe as the best system in your opinion (all vowels are short unless part of diphthong or marked long) is indeed a common choice if vowel quantity is indicated at all.
If you only prefer to use a breve to indicate that there is no diphthong, I recommend using the diaeresis instead; this is exactly what it is for.
With this adjustment your system is typical and therefore good for communication.
It is always good to know your target audience.
Some languages have letters like æ and ä, and readers unfamiliar with Latin are likely to parse those wrong.
If the audience is already familiar with the language, interference with other languages is far smaller an issue.
