1574 with the Siege of Nagashima
1590 with the Siege of Odawara
1600 with the Battle of Sekigahara
1603 with Tokugawa Ieyasu becomes shogun 1615 with the ending of the Osaka campaign

I don't think anyone uses the 1574 siege of Nagashima. Rather, they use 1573 with the ousting of the last Ashikaga Shōgun Yoshiaki from Kyōto by Oda Nobunaga without supporting another Shōgun, signalling the de-facto end of the Ashikaga Bakufu. Another frequent choice is 1568 when Oda Nobunaga entered Kyōto to place Ashikaga Yoshiaki on the position of Shōgun.

The difference here is periodization. While the Sengoku is defined as a period when central authority broke down and there was fighting between lords across Japan, the late 16th century is significantly different from the earlier periods in enough things that it should be treated separately. The usual way to do this is to call the period the Azuchi–Momoyama/Shokuhō period, after Oda Nobunaga (and his castle at Azuchi) and Toyotomi Hideyoshi (and his castle at Fushimi/Momoyama). There's then a question of when this period starts and ends. Should it start when Oda Nobunaga become involved in central politics, or when he ends the Ashikaga Bakufu? And should it ends when Ieyasu takes over in 1600/1603, or when the Toyotomi clan's destroyed in 1615? Running parallel to this question is that the periods of warrior rule is usually defined by the ruling Bakufu - Kamakura, Muromachi, and Edo. There's however a 30-year period between the de-facto end of the Muromachi Bakufu and the founding of the Edo Bakufu, so historians want a name to fill the gap.

The other issue is that if Sengoku is defined as a period when there's a lack of a central authority that over-rules everyone, regional lords fought each other, and the lower-ranking overtook those above them in a process called gekokujō, then when does that period end? Hideyoshi's unification of Japan in 1590 results in everyone needing to listen to him, so perhaps it should end there. But he wanted to invade Korea, the Toyotomi control doesn't last and there were still short fighting afterwards. So is Hideyoshi's unification of Japan in 1590 strong enough for us to label an "end" to the Sengoku, and if not, then what's the standard by which we should go by. The last period of conflict all across Japan in 1600? The founding of the next stable Bakufu in 1603? Or the last lord vs lord fighting in 1615? We can, and some do, even push the end to Shimabara in 1638.

Historians seems to be in agreement that it started in 1467 with the Onin War.

Actually no. Historians don't agree with this, the debate just hasn't permiated into popular culture in English.

The question becomes another about definition. Picking the Ōnin War as the start is actually very arbitrary. On closer examining of the era, historians have realized that the Ashikaga Bakufu still held considerable authority during and after the Ōnin War. It wasn't until the Meiō Coup of 1493, when Kanrei Hosokawa Masamoto overthrew the reigning Shōgun Ashikaga Yoshiki for Ashikaga Yoshitoo, resulting in two Shōguns at the same time did the Ashikaga Bakufu's control of the country really fall beyond repair. So if we define the Sengoku as a period without strong central authority, then the start date should be pushed forward to 1493.

On the other hand, if we define the Sengoku as a period of wide-spread conflict, then a strong case could be made to push the start date back to 1454 (the third year of Kyōtoku). That is when the succession crisis of the Kanrei Hatakeyama family finally came to blows and the Kyōtoku War broke out in the Kantō plains (technically broke out January 1455). Both were important conflicts that became significant factors to the outbreak of the Ōnin War. Heck, the Ōnin War could be considered an extension of the Hatakeyama succession crisis. The Ōnin War does present a step up in the level of conflict, especially in calling in clans from around Japan to the fighting of Kyōto and burning down significant portions of the capital. But given our definition of the Sengoku, there's no a priori reason why the Ōnin War should be its start. If we define the Sengoku as the late-Muromachi, we can even push the start date further back to the assassination of Ashikaga Yoshinori in 1441, the point where everything began to go downhill and regional conflicts became more pronounced.

The problem comes down to the fact that periodization, like other exercises in definition, is inherently arbitrary. Reality more often than not works on a sliding scale, and it's humans who want clear demarcations. There's no reason the early middle ages need to start at 476, and many threads exist to talk about the subject on the subreddit. On the other end, defining the end of the early middle ages to 1066 or 1000 or any other date would be just as arbitrary. There will never be agreement, and frankly, why does there need to be one? When writing things in depth, a scholar by necessity needs to give significant background on what came before to show the causes, and what came after to show it's effects, and all historical works would need to chose its own start and end date, all just as arbitrary but might make the most sense to the subject at hand.