They did! To one extent or another, almost every state during the warring states implemented reforms along the lines of Shang Yang, though in all likelihood none went as far as Qin.
As Eastern Zhou lost control over their vassals and warfare erupted between them, rulers and their ministers attempted to strengthen their states by any means necessary. This started as early as 685 BC, when Duke Huan of Qi appointed Guan Zhong as minister, and together launched a series of reforms to overhaul Qi. Going by the book that bears his name, Guanzi, he centralized the state, reduced the power of aristocrats, reorganized the agricultural basis of the country to support the military, disbanding the equal field system, appointing administrators and directly taxing peasants, and brought salt and iron under direct state control.
However, much of the book Guanzi appears to be written in later times, for example the concerns with salt and iron in all liklihood reflect Han dynasty era debates rather than concerns at the time. This is going to be a recurring theme here-the evidence for what happened just isn't very good. Too much time has passed, and too much has been lost. Another recurring theme, if Mark Edward Lewis is to be believed, is that specific reformers tend to be valorized to the point of overshadowing what was likely a more gradual process involving more people. Regardless of these caveats, Qi's reforms were successful, pushing them to become the most powerful state and first hegemon during the spring and autumn period. Following Qi's reforms, other states instituted their own changes, and continued to fight in a ever shifting set of alliances, at times trying to constrain any one state from becoming too powerful.
So if many states undertook reforms, what set Qin's apart?
To better understand that I'm going to jump ahead a few hundred years to state of Wei around 425 BC, which directly predecessed Lord Shang's in some sense, and also offers illustrations of the difficulties around reforms. In 424, Li Kui was appointed chancellor in the state of Wei, and instituted a set of reforms of agriculture and law as well as large scale government irrigation projects. He set small holding families to be the basis of agricultural development, pushed planting mulberries and other non-food crops in marginal lands, and instituted a system of state run granaries that would smooth fluctuations in grain markets and harvests by purchasing grain during good harvests and selling it when grain was expensive. He also reformed law and wrote the Canon of Laws, which doesn't survive. Excerpts from it on agriculture occur in enough other sources we know more about that, but on the broader topic of law we know very little of what he wrote.
This greatly influenced the later reforms in Qin. A Qin prince, who was in exile in Wei during the times of these reforms, returned to Qin in 385 to claim power after bitter infighting. This prince, Duke Xian, started reforms in Qin modeled after Wei. His son invited Shang Yang to Qin, to institute his more famous reforms. Lord Shang was also connected to Wei-he was working under a later prime minister when he was invited to move to Qin. His reforms would be inspired by and more sweeping than what came before: offering promotion into the lower nobility and land for soldiers who kill enemies, reallocating land, grouping the populace into self-monitering units of families, forcing people into these families by abolishing primogeniture and taxing adult males who live together, unifying weights and measurements, and more. We know more about his reforms than many of the other reforms of this period because the Book of Lord Shang survives and seems to have been written not too long after his time, and because fragments of Qin laws and bureaucratic documents have been found.
These suggest that the laws were not fully implemented to what is suggested in the Book of Lord Shang, but did to a large degree reshape life in Qin. Existing records of punishments were nowhere as harsh as both that and the Records of the Grand Historian suggest (though we could just be missing them), and that primogeniture still existed. At the same time, there are punishments for officials who are unable to adhere to the standardization of weights, farmland was distributed in square grids of fixed sizes, peasants really could advance based off of battlefield exploits (in one admittedly rare case, a slave was able to become a general), markets regulated, and massive state run workshops were constructed. These used slave labor consisting of prisoners of war and convicts, and produced everything from cloth to weapons to iron farm implements. The comprehensiveness of the reforms combined with some of the details that apparently don't exist elsewhere-such as offering soldiers the possibility of advancement instead of just monetary reforms-set Lord Shang's apart. This does come with the same caveat that we know way more about these than in other states, so it's possible many of them were, say, set out in the Canon of Law and lost to time.
This already suggests a few reasons that Qin was able to pursue greater, more comprehensive reforms than other states. The lateness of their reforms, at least partially caused by their position on the edge of what was then the Chinese world and small educated class, mean that they had a lot more to learn from. That they had a much smaller pool of potential administrators also made them more willing to accept immigrants from other states-all states at this time did, but Qin did to a far greater degree. This meant, again, they could learn more about what works and what doesn't.
One more story off branching off of the reforms of Wei illustrates other challenges-that of Wu Qi. Wu Qi also served under Wei, but had to flee to Chu after being accused of crimes. There, he too was made prime minister and launched his own set of reforms. However, after the death of Prince Daowang, aristocrats angered by his restriction of their privileges had him killed. Under traditional telling this derailed Chu reforms efforts and led to corruption and inefficiency, though recent archeological work suggests this may be overstated. None the less, it appears his death did lead to the end of more drastic reforms. While Lord Shang ended up in similar fashion, his reforms were complete and kept in place after his death. Drastic efforts to curtail the power of the nobility and increase that of the central state were risky, and opposition by the nobility could derail them.
They could also derail changes that had already taken place. In many of the states, efforts to redistribute land and centralize power were already quite old. Du Zhengsheng argues that by the time Qin was ascendant, the nobility had greatly weakened these reforms, enriching themselves and immiserating the larger populace. The rulers at the time weren't strong enough to over come this opposition.
On why they were unable to over come this opposition, Joy Chen collects a data set of the number and location of directly administered counties, versus counties that were given to essentially feudal vassals to run in the rulers name. Using the number of directly administered counties as a proxy for centralization, he theorizes, and collects evidence to show that external pressure lead to more decentralization, while being on the offensive supported centralization. This was due to the feudal vassals having more reasons to fight for their territory than administrators, while administrators had more to gain from the opening of new positions in conquered territory. Thus, the states of the central plains, under military pressure from multiple directions, may have found it harder to renew their reforms, while Qin being on the edge of the empire would be incentivized to aggressively reform.
The data on directly administered provinces is also interesting (from her paper). Early on, Chu is leading, which she suggests due to weaker preexisting nobles, but they fall off over time as further reforms fail and the royal house loses power relative to that of other states. Meanwhile, Wei holds steady while Qin rapidly creates new directly administered counties.
One final reason that Qin was more successful was their conquest of the (at the time) non-Chinese states in Sichuan. While the people of the former state of Ba were allowed some amount of autonomy, after attempting and failing miserable at rebelling, the state former state of Shu was directly controlled. Qin colonists poured into the state, some responding to state incentives to people of both Qin and other states, and others convicts or conquered subjects forcibly resettled. There, without any preexisting nobility to worry about, Qin was able to reform agriculture, attract peasants and industrialists, and build a massive irrigation system that still functions to this day. Outside of the increase in size and population and the geographical advantage they gained over Chu, Sichuan provided a test bed where Lord Shang's policies could be more fully implemented.
One final note, after Qin's took a dominant position among the various warring states, the rest of the states didn't roll over. In particular, Zhao launched their own set of drastic reforms. with their backs against the wall, squeezed between Qin, Wei, and the steppes, they adopted the military dress, independent cavalry, and horseback archery the steppes and drastically revitalized their military. They may have also pursued domestic reforms-the size of the armies they could muster in their final showdown, combined with the uptick in centralized counties suggests as much, though again direct evidence is sparse. In the end, though, sheer numbers and strategic failure on the part of Zhao would doom their efforts more than any failure of policy.