We have learned from the British experience in the 19th century and from our own in the 20th that it is cheaper and more effective to bribe countries to get what we want rather than to make war upon them. What makes it effective is that they know that we have the military power to use if the carrot isn't taken. There are a number of important benefits to us. Let's just take your example of Egypt.
Before 1973, Egypt was a soviet client state and avowed enemy of Israel. They were hostile to America and a threat to close the Suez canal to the West. At the end of the Yom Kippur War, in which American-supplied Israel completely outclassed Soviet-supplied Egypt . . . we turned them. Egypt agreed to make peace with Israel in return for getting Sinai back and American arms, support, and aid to replace the Soviets. In effect, America bought Sinai for Egypt for the sake of Israel. And it worked . . . cheaply and at a cost of zero US casualties.
The peace has lasted 40 years in the most warlike region on the planet. Here are the benefits to us.
1. Egypt has slowly transitioned from Soviet military equipment to American equipment. They are now dependent on us for spare parts, maintenance contracts, resupply, and logistics. This is huge leverage for us. Egypt can undertake a secret build-up without our knowledge. If they break the peace and make war on Israel, we can cripple their war machine within weeks by withholding parts, replacements, munitions, and technicians.
2. As part of the deal, US peacekeepers have been stationed in the Sinai and annual joint military exercises with the Egyptians has gone on for decades. We know their commanders. We know their capabilities. We now their limitations. They are using US tactics and US organization. This is more leverage. Our influence upon the Egyptian military is very big. They fought alongside us in the Gulf War. Their military wants to fight its next war with US assistance and support. They want no part of another war with Israel because of this.
3. Mubarak and Sadat before him made no problems for the US in all that time. The money and military equipment buys us much influence over the political leadership. And that has not changed. We learned in the Iran debacle of 1979 that it is senseless to back a dictator in the face of a popular revolution. We had bought much influence over the Shah over the decades, but kept backing him after he lost the will of the people. We have had nothing but trouble with Iran ever since.
4. The army is still the power in Egypt. They can take it over at any time. We have much influence with them. The new government of Egypt will be sorting itself out over the next decade or so and may change character many times. The army will remain consistent and may even take over again. Helping the Egyptian army retain control is a good thing for us and we maintain that by arming and supplying them. Whoever ends up in charge will be taking American arms, supplies, and assistance and we will have influence upon him. Morsi made that comment about boycotting American goods years before he was President and after Israeli airstrikes with weapons. Now that he's President, getting US weapons, and in position to actually do it, he hasn't said anything about a boycott.
5. The fucking Chinese are out there laying $Billions on third world countries trying to buy influence as well. We cannot allow the Chinese to have their way in the middle east.
6. The tanks and aircraft are built by Americans in America and a bigger market for them is good for the market and for our armament industry. The Chinese would love to give them with Chinese tanks and aircraft.