Seriously why everyone want to be rome so bad? Like its okay to just be the leader of your own big murderous empire without having to rip off Caesar again

Serious answer is that in an Western European/Mediterranean context, the Roman Empire essentially set the foundation — culturally, administratively and judicially — for what would coalesce into 'Western Civilization' and many statelets derived their legitimacy from being, in some form, a 'heir' to Rome and making such allusions were a tempting way to either consolidate rule or viscerally claim hegemony.

Some points to consider:

I. The popular notion of unwashed barbarians rolling over a decadent Roman Empire and putting to the torch centuries of progress is a fantasy primarily concocted and perpetuated by those with an unnuanced, chauvinistic view of history. Odoacer, who deposed the 'last Roman Emperor' Augustus Romulus was a Foederati (allied, semi-autonomous non-Roman auxiliaries/mercenaries) whose army included not just Germanic warriors, but a very large contingent of the Italic Roman military. When Odoacer seized Rome, he claimed to be acting on behalf of the Eastern Roman Emperor Zeno and to a lesser extent, the exiled Julius Nepos in Dalmatia. He retained the Roman Senate, paid lip-service to Zeno and even minted coins bearing himself and Nepos, took Roman titles and essentially preserved every practical and aesthetic fixture of the old Roman governance.

When Odoacer grew too unruly, Zeno would compel Theodoric — an Romanized Goth raised in the Imperial court —to supplant him. Once again, Theodoric preserved what was still essentially Roman governance in Italy and operated under the pretenses of essentially being a Viceroy of the Emperor in Constantinople. While his settled Goths would be subject to different laws than Romans, when Theodoric's ambitions and pretensions ran contrary to Constantinople, it was not a up-jumped barbarian seeking to shed a charade but rather a ruler who desired an quintessentially Roman primacy: Theodoric would restore Roman infrastructure, architecture and don the purple robes traditionally associated with Emperors.

The actual Western Roman Senate would last into the 7th century and it's titles as honorary dignities for centuries longer.

II. Though Post-Antiquity/Early Medieval histography is really vague and suffers from a lack of sources or really any defined knowledge whatsoever (for instance, nobody knows what the fuck really happened with or who ruled in post-Roman Britain for like a period of two hundred years until the Anglo-Saxons consolidated power, beyond conjecture and legend, it's wild) there's evidence to suggest that Western European feudalism and it's aristocracy may have been a direct evolution of remaining Roman administration rather than entirely replacing it.

The titles of 'Count and Duke' for instance, derive etymologically from the military stations of Comes and Dux. As late as the 6th century, the historian Procopius reports that the Limitanei (Roman garrison troops who may or may not been the nucleus of what would later become the feudal levy, subject of dispute) retained visible Roman heraldry and military traditions to the point where they could even be 'recognized as belonging to the Legions they were assigned when they served in ancient times.'

III. As stated previously, claiming the mantle of Emperor was a manner through which to solidify legitimacy and firmly establish a sort of semi-universal hegemony over Christendom. Most infamously, Charlemagne would be crowned Emperor by the Pope and after the Carolingian Frankish Empire collapsed, the Imperial title would be tossed between a series of local Italian magnates who essentially extorted/'protected' the Pope, until Otto I, King of Germany, would conquer swaths of Italy and receive the imperial dignity, which was also another useful way to control the powerful church as the Emperor was (arguably) seen as senior to the Pope until the Investiture Controversy. The Kings of Leon and Castille would also proclaim themselves as 'Imperator totius Hispanie' or Emperor of all Spain, but wouldn't really be taken seriously and the title gradually fell out of disuse.

IV. The Eastern Roman, or Byzantine, Empire remained one of the most powerful states in Europe and it's periphery for centuries and it's influence would be extensive. Many powerful Viking and Anglo-Saxons served in the Varangian Guard, such as Harald Hard-Ruler of 1066 fame, disseminating their ideals and notions of 'Roman-ness' further. Orthodox Christianity and Byzantine cultural influence would come to Russia by virtue of it's Viking rulers, who came into contact by raiding, trading and fighting as mercenaries for the Byzantines.

The ruling Russian dynasty would be tied to the Byzantines by blood, via several Imperial marriages, and faith. When Constantinople was annexed by the Ottoman Empire, Ivan IV (the Terrible) would emphasize the power of his burgeoning state — which had already adopted Byzantine, and thus Roman, titles, ceremony and symbols such as the famed double headed eagle — would proclaim himself Tsar, which literally translates to 'Caesar' which had long shifted from meaning from simply being the name of Julius Caesar but a title synonymous or even identical to Emperor.

Moscow would become a 'Third Rome' as the successor to the Byzantines in primacy of the Eastern Orthodox world which fed mutually into their claims of Roman Imperial status.

The Ottoman Sultans took the title of Kayser-i Rum, moreso to denote their dominion of the Greeks and other peoples of the Balkans (who still identified as such) though the degree to which they viewed themselves as 'successors' to Rome were disputed even contemporarily, and the title eventually fell out of active use and became lost in the sea of self-important appellations ascribed to the Sultan.

V. Influence of the Church, which was one of the few persuasive entities that gave European states a common foundation. The Roman Catholic church has it's foundation as we know it with the rise of Constantine I who would make it the official state religion of Rome. It spoke Latin, which disseminated as the Lingue Franca, carried on customs derived from Rome and leveraged this continuity by exercising the power to crown (in the West) Roman Emperors.

VI. The Renaissance would see a renewal of interest in Roman culture, arts and architecture. Rulers would pose for portraits depicted in Roman-style cuirasses, prize Neo-Hellenic style marble works, and Kingdoms as far flung as Poland and Sweden which had never been under Roman rule or even shared a border would mint coins bearing the visages of their ruler with Latin text and in a Roman style.

Roman history would become increasingly politicized, especially as the era of European colonialism approached. Edward Gibbon would be the progenitor of the myth that Christianity caused the fall of the Roman Empire, not as a jab at the faith itself but the Catholic Church, as he hailed from the Protestant England. European Kingdoms asserted to be successors of Rome not just in titles, heraldry, culture and law, but as inheritors of the torch of 'civilizing' duty which it leveraged to justify imperialism. It became useful, in the Western European cultural narrative, to frame the fall of Rome as a clean wipe in 476 and themselves as direct successors rather than acknowledging the Eastern Roman Empire and the less-romantic reality.

tl;dr:

The Roman Empire in the West didn't fall in 476 to begin with so much as had their institutions co-opted and continued to materially exist for centuries afterwards before said institutions eroded. The Church was pervasive and benefitted from perpetuating Roman derived language and customs long after it's fall, and the most powerful rulers did the same and claimed the Imperial dignity. Neighboring territories never apart of the Empire adopted much of this due to osmosis. The Renaissance and similar 'intellectual revival' movements threw more fuel onto the Roman fetishism fire.

The confluence of these factors would essentially result in an entire continent of Roman-clout chasers.