With the exception of Father's unexplained continuation of the FEV program. The Institute's experiments do have a point.
The Warwick Homestead initiative is a test of improving crop growth and agricultural efficiency on the surface, for the eventual future in which The Institute emerges. Along with plant growth improvements they could immediately use to increase food production in Bioscience.
The Watcher program is a spy program. Meant to ensure the Institute has an extensive network of spies and informants, some which are Synths others which are human, to identify and report on possible threats to The Institute.
The Synth program is two-fold, to ensure they have both a military contingent without risking their own people, and a labor force.
Phase-3 is meant to ensure they always will have enough power to meet their needs, and will be energy self-sufficient.
Etc.
Ultimately The Institute's goal is the same as the Enclave's: survival and protection of its own people. The primary difference is The Institute, under Father, want to wait the surface-world out all while building up their underground science utopia: believing the surface is eventually doomed to extinction anyway. The Enclave on the other hand, believe in taking an active roll in ensuring the wasteland arrives at that same extinction much quicker.