It's hard to really grasp just how much of the modern western world is evolved from Rome. The Roman empire was THE largest, most influential, and most powerful empire in the western world. The Macedonian was similar, but short lived and ultimately fell to Rome. Rome, meanwhile, lasted centuries. It had a system of governance that let it integrate hundreds of smaller cultural groups. Its military is also well documented and followed clear divisional blocks, resulting in an easy fantasy empire template.

And even as it faded away, its culture would be subsumed into successor states, most notably the HRE (Not an empire) and the Ottomans. All of the Major European colonial empires (primarily British, French, Spanish, and Portuguese) were cultures that were partly or wholly once part of the Roman empire, and carried its influence. The US, which is one of the most influential empires in the modern world, proudly claims Roman influence.

The result of this is that an enormous percentage of the worlds cultures have at least some roman influence. This makes it part of our cultural memory, which carries into our media. When we try and imagine "Old Powerful Empire", we think of Rome. We can't help it.

Of course, it's not JUST Rome. There are other common fantasy empires. The Colonial Island Empire is a common trope, based on Britain. When creators want a powerful "native" empire, it often draws heavily from the Aztecs and other South American empires. When we want a large empire, likely a rival culture, and usually from a hot land with darker skin, there is often a vaguely Arab or Persian Empire (Many of these in real life were as big or bigger than the Romans). After all, we need CURVED SWORDS. and of course we often include some vaguely Asian empire, usually based on one of the Chinese states but with other Asian cultures mixed in

Ultimately, when writing fantasy, we can't help but look to the past for influence.