Biomembranes are complex materials composed of lipids and proteins that compartmentalize biochemistry. They are actively remodeled in response to physical and metabolic cues, as well as during cell differentiation and stress. The concept of homeoviscous adaptation has become a textbook example of membrane responsiveness. Here, we discuss limitations and common misconceptions revolving around it. By highlighting key moments in the life cycle of a transmembrane protein, we illustrate that membrane thickness and a finely regulated membrane compressibility are crucial to facilitate proper membrane protein insertion, function, sorting, and inheritance. We propose that the unfolded protein response (UPR) provides a mechanism for endoplasmic reticulum (ER) membrane homeostasis by sensing aberrant transverse membrane stiffening and triggering adaptive responses that re-establish membrane compressibility.