You can try a 1-frame link yourself by trying to combo one of your heavy autodoubles into a 5-frame normal (for most characters, all light normals are active on the 5th frame. For some characters, only standing LK will work). It’s tough.
The heavy autodouble will only keep your opponent in hitstun for 5 frames after you’re able to perform new actions - if you do a light normal on the very first frame where you can act, it’ll combo. A frame too early and your input will be ignored and no attack will come out, and a frame too late and your opponent will be able to block your light normal.
This is particularly important if you’re trying to cancel that light normal into say, a dp ender - if you’re successful, your combo will go as planned. If you’re too late with your link, they block your normal and your dp and punish. Too early and you don’t even get out your normal; instead, you get a delayed regular dp which can be blocked and punished.
Kilgore’s standing MK is also +5 on hit - people can theoretically link a 5-frame normal after it as a 1-frame link, special cancel, and get a combo. But few would try this, because if they mess up and their special is blocked, they will get punished. Instead, they might try to link off of a counterhit stMK, or a meaty stMK on an opponent on their getup - because now the stMK is more than +5 on hit, and it becomes, say, a 3-frame link. Much more reliable.
You might see similar situations in old tournament play of Evil Ryu in Street Fighter 4 - his go-to BIG DAMAGE combo involves an axe kick special which leaves him 4 frames of advantage in which he can connect one of his 3-frame or 4-frame normals (so, a 2-frame or a 1-frame link).
Many players would cancel this normal into a special move (his tatsu) which allows them to continue the combo and get that BIG DAMAGE if the link is successful - but if they fail and the tatsu gets blocked, they can be punished. There have been tournament upsets where even top players like Daigo dropped this combo at critical moments and lost matches because of it.
Since then, players have practiced a form of buffering in SF4 called plinking (which allows a button to be treated by the game as being pressed on 2 consecutive frames rather than a single frame) to make it more consistent (as now it can be as much as a 3-frame link rather than a 2-frame link).
In addition, they now all use a 3-frame normal and then link it into another normal before special cancelling - so rather than betting that they performed the hard part correctly, they give themselves time to identify that they did so, as well as more overall damage. Even the button layout meta changed for some players to accommodate for easier plinking methods.
Essentially, the playerbase worked hard to make the 2-frame/1-frame gap wider, and changed the combo to make dropping the link much less dangerous. This is because 1-frame links are so risky even to the most practiced players - as you have to play so consistently in tournaments, it’s better to work around them than rely on precise timing skills.
Many casual players at the time were also very against the mentality of 1-frame links becoming prevalent in fighting games - if even sponsored top players can lose matches because of them, how much practice would a normal player have to do to consistently perform even bread-and-butter combos, online no less? It could be seen as deliberately kneecapping players who don’t have a lot of time to invest in the meta and in practice.
This is probably a large part of why SF5 introduced a natural buffer to avoid 1-frame links being in the game (if you’re 1 frame early or late on a link, the game fixes it for you, I believe) - to encourage casual players that nothing is being held out of their reach.
Funnily enough, desk’s combo vids still found a way to bring back 1-frame timings - by using attacks in combos which hit opponents at the same precise frame where they are hit by a projectile which would launch them, and the game causing them to stay grounded. But he’s just crazy like that, and do they even count as 1-frame links any more?