The Goths population was a small percentage of the rest of the Roman population. Even though Theodoric passed laws against inter marriage with the Romans, they would have eventually been absorbed into the Roman population. He was actually quoted as saying we cannot stay here because we will lose our identity as a distinct people.
By the way they never called themselves "Ostrogoths". This is a term the Romans and historians used to identify the eastern and western groups of Goths. There were a lot more around than those 2 groups. An Italian author referred to them as Valagothi. Because they followed Theodoric, descendent of Valamir, the 1st of the Amali royal family. That Royal family only survived 3 generations before it disappeared.
The only way the "Ostrogoths" could have survived was to join their cousins the western group of Goths in southern France. A good number of them actually did this and refused to follow Theodoric down into Italy.
One interesting fact from the book I am reading, Empires and Barbarians, by Peter Heather, There was a very sharp increase in the Gothic population from the 2nd to the 4th century. Their numbers may have approached a half a million. This included 2 new groups of Vandali that spoke the Gothic language. They were called the Astingi and the Lacringi. In addition, Gothic speaking Heruli, Gepids, Taifali and Rugi were part of the Gothic nation.
The author of this book believes that the Romans were responsible for the great upheavals of the Gothic populations when the Huns appeared. The Romans made repeated attacks on the main Gothic group called the Tervingi. This was the largest and most powerful of the Gothic Chiefdoms. These attacks destabilized the political leadership of the Tervingi. They had a council meeting and decided to ask for asylum inside the Roman territory. There were a least 5 more major political entities of Goths. probably numbering 50,000 to 75,000 each. They were spread all the way up and down the east side of the Carpathians. Also along the north coast of the Black sea and 1000 kilometers east. The author believes the Huns numbers were exaggerated. He believes that if the Tervingi were not disrupted, that the Goths could have crushed the Huns. Virtually annihilating them. So the Romans were responsible for their destruction at the battle of Adrianople.