Why would it? Of course, probably Byzantine Empire would be better off without its OTL Norman neighbors but that's pretty much it.
This completely changes Byzantine history.
Without the Normans, Alexios' attempt to reclaim Anatolia from the Seljuks Turks isn't delayed until 1097, but can possibly begin 16 years earlier, in 1081. That's only ten years after Manzikert, meaning the Turks are less well established. By 1097, it has been 26 years, a whole generation has passed and arguably it's too late.
What's more, the battle of Dyrhachium never happens, meaning the professional Byzantine army isn't destroyed. This in turn means Alexios isn't reduced to rounding up Balkan peasants and creating a new army from scratch. It also means that the Pecheneg invasion of the Balkans may not happen, freeing up the gold that Alexios was forced to spend on hiring a Cuman army to defeat them.
The upshot of all this is that the Byzantines will have a substantially more powerful army and more gold, as well as a 16 year head start, to take back Anatolia. Their enemy will be fewer and less well entrenched. Obviously, this will affect the frontiers in favour of the Byzantines, most likely with critical results. I predict the empire reclaims Anatolia.
This then totally changes later history. Istanbul may well be the capital of Greece today, and the nation of Turkey will not exist. The modern world is unrecognizable, because the Ottomans also never happen. That totally changes the middle east. Israel is never created. Syria, Iraq and Jordan don't exist either. Nor does Saudi Arabia. Nor Kuwait. The impact is vast and incalculable.