All commonly-used bicameral Latin-script typefaces use ascenders (portions of a glyph that rise above the typical upper-limit height for glyphs of the character type under consideration) and descenders (portions of a glyph that dive below the baseline that forms the normal lower limit for glyphs of the character type under consideration) on a selection of their lowercase letters (and sometimes on some of their numeric digits as well):1
(Lowercase Latin F, showing an ascender; in this typeface, the normal upper limit for lowercase letters is level with the top of the F's crossbar.)
(Lowercase Latin J, showing a descender; the tail of the J swoops well below the baseline where most letters sit.)
(Lowercase Latin thorn; this letter has both an ascender and a descender!)
(For comparison, here's a lowercase Latin Z, with neither ascender nor descender.)
Ascenders and descenders are used because they make text vastly easier to read, by making different letters more visually distinct from one another (when your eyes are moving along a line of text, the ascenders and descenders sticking out above and below stand out); although (as @BillyKerr's answer points out) the ascenders and descenders did not originally come into being as reading aids (instead being artifacts of the descent of the lowercases from the cursive and semicursive scripts of the post-Roman era), the improvement in readability that they provide is so great that attempts to eliminate ascenders or descenders, such as Philip Rusher's 19th-century Banbury typefaces, have universally met with failure.2, 3
Yet, despite this major advantage of using ascenders and descenders, their use is almost completely confined to the lowercase letters (and sometimes the numbers). Of the capital Latin letters, only Q (with its tail), and sometimes J as well (with its bottom hook), are regularly equipped with descenders, and ascenders are completely absent.4, 5
(Capital Latin Q, with a descender - a rarity among its kind.)
This renders lowercase or sentence-case (which is almost-entirely lowercase) writing much more readable, especially in a hurry, than all-caps writing (which is why road signs, for instance, are usually in sentence case nowadays) - ironic, given that one of the main reasons for writing in all caps is to draw attention to important things that you want to be certain are understood!
It seems to me like it should be simple to solve this problem by putting ascenders and descenders on capital as well as lowercase letters, bringing the readability of the capitals up to par with that of their lowercase counterparts. The existence in the wild of successful typefaces with descenders on Q and J shows that it's perfectly possible to put a descender on a capital letter, and ascenders shouldn't be much (if any) harder. A number of possibilities immediately suggest themselves (the peak of an A poking up above its neighbors; the curved bulk of a C arcing above cap height and back down to the right; an F punching its tail through the baseline and down below, jacking up its upper bar past cap height, or both; a G swooping below the baseline and back up again on its way to the folded bit at its lower right; an I projecting its head and shoulders above the rest; K or R stretching their legs on below the baseline and beneath the letter following; an N poking its pointy bits through both the cap height and the baseline; the upper and lower bulges of capital S bulging past their former upper and lower limits; V sticking its pointy butt through the baseline; X taking a note from Greek chi and sinking its lower prongs into the ground; etc., etc., etc.).
So why are ascenders and descenders on capital letters essentially unheard of in common typefaces (with the exception of Q, and, less-commonly, J)?
As suggested by @TKoL in the comments, I've put together a basic font to demonstrate what I've in mind (and gotten much more proficient with FontForge in the process, yay!); here's my first test of the font. My first impressions are that it does make all-caps words more readable (although the spacing between letters still needs tweaking), at the expense of (as expected) requiring slightly-greater line spacing to keep the lines of text from running together.
2: This is not limited to the Latin script; one of the reasons (although far from the only one) that the Deseret alphabet was such an abysmal failure was its total lack of ascenders and descenders, which made all words look alike and made reading the script difficult and fatiguing.
3: In contrast, typefaces with reduced-height-but-still-distinct ascenders and descenders are quite successful; Liberation Sans is actually a perfect example of such a font. Note how a letter without ascenders or descenders, or the non-ascender-non-descender part of a letter that does have them, already comes up most of the way to the top of the line (especially when you consider that the normal height of the top of a capital letter, or even the [somewhat-higher] normal height of the top of an ascender on an ascending lowercase letter, is actually well below the upper horizontal line in the FontForge glyph editor); in an older-style typeface, the ascenders and descenders would go much further up and down, and the eye of, say, a lowercase B or P would take up only half, or even less, of the total line height, just as occurs in handwriting (and there to an even greater extent, with the eye of a handwritten lowercase D or P or Q or thorn or B easily shrinking to less than a third of the total line height, judging from my own handwriting, or at least what of it I can still read).
4: This, too, is a problem not limited to the Latin script. The Greek alphabet uses ascenders and descenders even more enthusiastically on its lowercase letters than does the Latin alphabet descended from it, with a greater proportion of its letters having at least one (to the point that the Greek script has a greater total number of ascending or descending lowercase letters than does the Latin, despite having fewer letters in total) and with a greater variety of forms seeing use, but the Greek capitals have not a single letter with either (even worse than the Latin script, which at least has Q and sometimes J). The Cyrillic alphabet is less affected (its lowercases have fewer ascenders and descenders among them to begin with - Cyrillic lowercase letters tend to be shaped much more like their capital forms than do Greek or Latin lowercases - and a handful of its capitals hang onto their descenders), but, even here, there are more ascenders and descenders among the lowercase letters than among the capitals.
5: Interestingly, letters that entered the Latin script after the Roman era seem more amenable to having descenders even as capitals (though still not ascenders): capital wynn, Ƿ, capital ezh, Ʒ, capital yogh, Ȝ, capital yr, Ʀ, capital gamma,6 Ɣ, and capital vend, Ꝩ, are all equipped with descenders in at least some typefaces,7 as is the Sami form of capital eng (although the more common African form, Ŋ, used by most fonts,8 is not).
6: Not a typo - gamma is actually used in the Latin alphabet by some African languages.
7: Leading one to wonder why thorn, which came from the same source as wynn at around the same time, lost its descender!
8: ...including Liberation Sans.