So I'll take a stab at this, but I'm afraid there isn't going to be a satisfying answer. And my academic English isn't well practiced right now. I'm a linguist and I specialize in historical linguistics and phonology, so the etymology of surnames is something I've studied.

Surnames have developed in different ways at different times throughout the world, so I'm going to ignore a lot of information and just focus on England since we're dealing with English surnames. Normans brought the practice of surnames to England in 1066. There were several options for strategies to surnaming that are common to the western world that England also followed: 1) your surname was your occupation (Smith, Fletcher, Cook, Taylor, Turner, Knight, etc.). 2) your surname was the place where you lived. This could be a very specific place in the case of wealthy land owners, the name of a castle for example (this is/was a strong tradition among nobility), or it could be slightly more generic like the name of a town, lake, river, mountain etc. (Preston, Hilton, Stanley, Thames ). Or it was even more generic and was just the name of a "nearby" geographic feature without a proper name (Heath, Dale, Hill). Some in England used their father's given name as their surname (Johnson, Davidson, etc.). They could even be strictly descriptive (Redhead, Black, Little, Armstrong). This is not an exhaustive list of strategies, but these were the most common.

However, for a long time, these names were not fixed. If you changed occupation, or moved, then you changed your surname. It wasn't until the 1400s that this system becomes mostly stable and strictly hereditary.

Now, having the last name of a cardinal direction stems from the "generic place name" strategy. People would've chosen them because they lived or were from "north" or "west" of something, probably in or near a town, or a prominent geographic feature and more rarely for having immigrated from one of those directions. So it's impossible to say *specifically* what each instance of this surname referred to. The name "West" was for example most common in Essex, which is as far east as you can be in England! "South" and "East" aren't particularly common, but language has evolved dramatically since the Norman conquest and other forms do exist such as "Eastes," "Estes", and "Este." For "South" there exists a large number of variations ( Soth, Sother, Sotheron, Southers, Southern, Soutt, Soot, Soots, Sowte, and Zute, there also exists variations of a different sort in surnames like Sutherland, or Southard).

If you were to add up all the possible variations that exist for South and East, I bet the numbers get much closer. Any remaining difference is just pure chance. People weren't given cardinal direction surnames in equal numbers, and those families haven't passed down the names in equal numbers. Which names survive and which dwindle is largely just chance, and this is true for all surnames. Obviously, certain surnames, like common occupations such as "Smith" have an edge but otherwise there was no method to giving everyone surnames. It was a free and chaotic process. So I'm afraid, there isn't a specific reason.

Fiennes, J. (2015). The Origins of English Surnames: The Story of Who We Were. Robert Hale.

Hough, C. (2018). The Oxford Handbook of Names and Naming (Oxford Handbooks) (Illustrated ed.). Oxford University Press.

Edit: I probably should've refreshed the page every now and then while typing all of this up. /u/desGrieux already covered most of what I'm discussing here.

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I think this has a lot to do with (historical) linguistics, so studying linguistics, I think I might be able to answer this.

The people whose descendants would pass on names like West or North didn't always use surnames. The Anglo-Saxons, like most Germanic people, originally had one given personal name. These names were more or less unique combinations of recurring elements (Æthelred means 'noble counsel'; Æthelwulf is a 'noble wolf') and were mostly not reused in communities, so that this one name was sufficient to definitively identify a person.

This only changed when the Anglo-Saxons came into contact with other peoples: the Norsemen and, later, the Normans. They brought with them their names and, importantly, their naming philosophies. Instead of relying on the constituents of the name (nobility, honor, strength, wolfs, ravens), they reused names of powerful figures so as to imbue the same characteristics of these honored ancestors onto their children. Multiple children having the same name leads to problems of identification, however. "Which Erik are we talking about again?" The obvious solution was to give by-names, i.e., secondary names derived from an identifying characteristic. "You know, Eric the smith, Eric, the son of John, Eric with the brown hair, Eric who lives near the woods, or, of course, Eric who moved here from the North." I'm sure you can guess which surnames evolved from these characteristics. (As a fun aside, if your last name is King, your ancestor likely wasn't a king. Names of this type were most often derisive nicknames, mocking people acting like they're better than others.) These by-names stuck around and slowly evolved into the system of surnames in use today. In Germany, for example, this process was abetted by people moving into towns. In these larger settlements, there'd of course be more than one Wolfram or Martin. These newcomers were often identified by whence they came (a region, another settlement, or just the general direction).

So now that we understand why the cardinal directions turned into surnames, why are East and South less common than North and West? Well, that's where linguistics comes into play. As I explained, the process of acquiring surnames started when the Anglo-Saxons had prolonged contact with the Norsemen and the Normans, i.e., the time from the 8th to the 11th century. And people in the 8th to 11th century spoke a version of English that is quite different from the one in use today. Let's look at the Old English (OE) words for the compass directions (OE forms taken from the Oxford English dictionary):

North -- norð (ð being a ligature for a th-sound)

West -- west

South -- suð

East -- east, eastan, æst (æ being a ligature for the a-sound in, e.g., 'cat')

As you can see, if we ignore the ligatures for a moment, the words for North and West changed much less than those for South and East. This means that there are a lot of surnames derived from the latter two that don't make this etymology obvious. Aston is someone from an eastern place, for example, and the Sutherlands at one point in time lived in southern lands. Sutton is someone from a southern enclosure, i.e., a settlement or town ('town', like '-ton' comes from 'tun', a word describing an enclosed settlement -- cf. German 'Zaun' meaning 'fence'; 'tun' can also be a generic name for any settlement). So while someone from the North or West might have been called exactly that in 900 AD, someone from the South or East might have received a name much less familiar to us now.

There could of course be different reasons that other people might be able to explain. But I hope that I have illuminated some of the linguistic processes that likely have contributed to the discrepancy that we find today.

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Sources:

Leslie Dunkling (2015): Collins Dictionary of Surnames. From Abbey to Mutton, Nabbs to Zouch. New York: Collins-Harper.

John Titord (ed.) (2009): The Penguin Dictionary of British Surnames. London: Penguin.

I got a follow-up question. Why are certain combinations of “direction + some other word” are more common than the others? What I’m talking about is that surnames like Westwood and Eastwood are more common than Northwood and Southwood or Southgate being more common than Northgate/Westgate/Eastgate? Is there any logic behind it or it’s just a coincidence?