What is case?

The discussion both in this question and in the one it inspired on ELU seems to conflate two distinct meanings of ‘uppercase’ and ‘lowercase’:

Based purely on shape and size, originating in whether a glyph was originally usually stored in the typographer’s upper or lower case (= drawer). Based on functionality, describing what upper- and lowercase letters are used for in modern-day English.

When we think of uppercase letters, we no doubt think of both of these at the same time: A is not only recognisable as something that is distinct in its form and shape from a, it is also distinct in that it is used at the beginning of sentences, in acronyms, to start names, and (in good taste or not) for emphasis and headers.

Numbers are a somewhat different matter, though. If we define case by (1) alone, then it makes perfect sense, as in Vincent’s answer, to say that lining numbers are ‘uppercase’, while text numbers are ‘lowercase’—the picture linked to by curiousdannii even shows that the different styles of letters were frequently kept in the upper and lower cases in typographers’ kits.

But if we define case in terms of function, it is abundantly clear that lining and text numbers do not correspond to upper- and lowercase letters. The use of one or the other type of numbers is dependent on entirely different things, and they are never mixed the way upper- and lowercase letters are.

Unlike Vincent, I consider the functional aspect very central in the modern-day definition of what ‘case’ is, and I consider that lining and text numbers are not ‘upper-/lowercase numbers’, at least not as we would normally understand that. In other words, as presupposed by the question, that there are no upper- and lowercase numbers for the present purposes.

Why is case?

The original shapes of the letters of the alphabet (all the way from Egyptian hieroglyphs through Phoenician, Greek, and eventually Latin) were what correspond more or less to our current uppercase letters. They are thus the ‘default’ letters, historically speaking. They were made originally for scratching, etching, hewing, engraving, and otherwise writing on very solid materials: stone, wood, clay and wax tablets, etc. The fact that writing in these non-cursive letters is quite slow didn’t matter much, because writing in the materials available was much slower in itself. At this point, the alphabet was unicase.

Cursive forms of the letters arose (some from variant forms of the previous unicase glyphs, some from inventions, some in various other more or less complex ways) when more sophisticated ways of writing became available and writing in big, heavy block-glyphs became too time-consuming. In other words, when the bottleneck had moved from being the material used to being the glyphs used.

Initially, these cursive letters were simply variants used when quick writing was desired; for more ‘formal’ writing (engraving on statues, etc.), the older non-cursive forms were still used. The alphabet was still basically unicase, since the two different ways of writing were not mixed—they were basically like two different fonts.

It wasn’t until much later (I’m not sure exactly when, but some time between the 7th and 12th centuries, approximately) that the two letter styles really began to be mixed together in a system more or less comparable to our current upper- and lowercase one.

Why no numeric case?

This leads us to the actual question: why did no cursive (= lowercase) numerals begin to emerge along with the lowercase letters?

No authoritative answer is likely to emerge on that count, I’m afraid—the full reasons are lost in history. I would venture the following hypothesis, however:

When cursive letter forms began to emerge and be used as an alternative writing style (in Latin, some time during the first century BC), the Arabic numbers—themselves borrowed from Brahmic scripts in India—had not yet been borrowed; they used Roman numerals instead, which were just letters and thus had cursive variants

At some point, Arabic numerals were borrowed and started supplanting Roman numerals

While the cursive and uncial styles were in concurrent but complementary use, cursive and uncial styles of the Arabic numerals developed that each fit their own letter style

When eventually the modern case system emerged from these two variant styles, the function that was attributed to both was not really felt to be relevant for numbers (write a name with a capital number? Begin a sentence with a capital number?), so they continued to be just variants of each other, to be used where their shape fit best

Addendum: other scripts

Uppercase letters have one more function that has not been mentioned: clarity and disambiguation. For example, when filling in a form, it is common to see “Please write in block letters only” or something to that effect, to make sure that what you write is clear and legible and cannot be mistaken for something else.

To some extent, we do have ‘uppercase’ or ‘block’ numerals for this function: I (one) gets a serif at the top (1) and a horizontal stroke at the bottom (1̱); 7 gets a middle stroke (7̵) to disambiguate it from 1; 0 (zero) gets a slash through it (0̸) or a dot inside it (can’t figure out how to display that here) to disambiguate it from the letter o.

Some scripts that do not distinguish case do actually have a distinction in numerals that mirrors this. In Chinese, for example, all numeric characters up to 10,000 (i.e., all the characters you need to write up to 99,999,999) have two forms: a ‘short’ form and a ‘long’ form. The long form is used when absolute clarity and nonambiguity is necessary, e.g. on cheques (where they also help prevent fraud by adding an extra stroke to make a 1 a 10), here given in simplified characters as short form / long form (the bullet at the beginning is zero):

〇 / 零 一 / 壹 二 / 贰 三 / 叁 四 / 肆 五 / 伍 六 / 陆 七 / 柒 八 / 捌 九 / 玖 十 / 拾

百 / 佰

千 / 仟

万 / 萬

Interestingly, the difference between these two styles is known as 小写 xiǎoxiě ‘little writing’ and 大写 dàxiě ‘big writing’, which is also the terms used to translate the Latin alphabet–based notions of ‘lowercase’ and ‘uppercase’.