Learning-based techniques have significantly improved the accuracy and speed of deformable image registration. However, challenges such as reducing computational complexity and handling large deformations persist. To address these challenges, we analyze how convolutional neural networks (ConvNets) influence registration performance using the Horn-Schunck optical flow equation. Supported by prior studies and our empirical experiments, we observe that ConvNets play two key roles in registration: linearizing local intensities and harmonizing global contrast variations. Based on these insights, we propose the Encoder-Only Image Registration (EOIR) framework, designed to achieve a better accuracy-efficiency trade-off. EOIR separates feature learning from flow estimation, employing only a 3-layer ConvNet for feature extraction and a set of 3-layer flow estimators to construct a Laplacian feature pyramid, progressively composing diffeomorphic deformations under a large-deformation model. Results on five datasets across different modalities and anatomical regions demonstrate EOIR's effectiveness, achieving superior accuracy-efficiency and accuracy-smoothness trade-offs. With comparable accuracy, EOIR provides better efficiency and smoothness, and vice versa. The source code of EOIR is publicly available on https://github.com/XiangChen1994/EOIR.