If Israel had kept the Sinai Peninsula, it would have had a significant impact on the regions history. The Sinai Peninsula is rich in energy, meaning that trading its ownership would greatly weaken Egypt and strengthen Israel, particularly in the area of economics and foreign policy. The territory of the Peninsula is many times that of Israel itself, supports an excellent tourist industry, and would give Israel land directly bordering the Suez Canal itself, which would again be excellent for Israel. Israel would have control of the Suez Canal, one of the most important sea canals in the world, which would give it a huge military advantage because its allies could have better navy access to the Mediterranean and Red seas, and also an economic boost as well. However, it is also possible that the Egyptian people in Sinai would have tried to revolt and join Egypt again, which could lead to even more public outcry and strain on Israel. This could have possibly led to another pan-Arabic war with Israel.
It is important to note that Israel did occupy the Sinai Peninsula after the Six-Day War in 1967, but returned it to Egypt in 1982 following the implementation of the 1979 Egypt-Israel peace treaty, which saw Israel return the region to Egypt in exchange for the latters recognition of Israel as a legitimate sovereign state.
Overall, it is difficult to predict exactly what would have happened if Israel had kept the Sinai Peninsula, but it is clear that it would have had significant implications for the regions history and politics.