What makes you think that the eastern Roman or "Byzantine" army was helpless against cavalry?
What makes you think that heavy cavalry and heavy infantry would be useless against enemy cavalry forces? What makes you think that the "Byzantine" army didn't also have light cavalry and light infantry, etc., etc.?
Here is a link to an article about "Byzantine" military manuals:
Have you read any of them and what they say about the strategy and tactics to use against different types of enemies with different tactics?
Why do you assume that the Turkish invaders of Asia Minor were some sort of tactical super warriors who were invincible against the "Byzantines"? The Battle of Manzikert was a defeat because the Roman army was not very loyal and cohesive and some of the commanders traitorously failed to do their duties. After Manzikert the Turks took over almost all of Asia Minor because the leading "Byzantine" politicians were too busy fighting for power to do anything to defend against the Turks.
Here is a link to an article with a table listing estimates of the area and population of the eastern Roman or "Byzantine" Empire at various times.
Note that in 1097, 16 years after the Battle of Manzikert in 1071, the population is estimated at 5,000,000 people and the area at 555,000 square kilometers.
In 1143, only 46 years later, the population has doubled to about 10,000,000 people and the area has increased to 950,000 square kilometers, an increase of 71 percent in size.
So the eastern Roman or "Byzantine" empire seems to have had a lot of political and military success in the period of 1091-1143, considering that it doubled its population and increased its land area by 71 percent.
Here is a link to a map of the "Byzantine" Empire in 1025:
Here is a link to a map of the Roman or "Byzantine" Empire in 1081, when Alexios I Komnenos became emperor:
Note that by then the Turks have conquered almost all of Asia Minor.
Here is a link to a map showing the Roman or "Byzantine" Empire in 1180:
Note how much the Roman or "Byzantine" control of Asia Minor has increased.
Obviously there were a number of battles, sieges, campaigns, and wars between "Byzantines" and Turks during the period of 1081 to 1180. Considering how the map changed between 1097 and 1180, which side would you estimate was the usual winner in such conflicts?
If matters had gone just a little bit better for the Romans or "Byzantines" during that period, EmperorCinnamon would probably speak Greek and consider themself a Roman citizen.
So the idea that Turkish tactics were invincible against the "Byzantines" seems to be a little bit inaccurate.