Why did some scholars and Companions refrain from using mounts despite their availability, and does this contradict the concept of taking lawful means and utilizing time and effort for other matters?

There are narrations indicating that walking to certain acts of worship is better than riding, such as walking to congregational prayers, Friday prayers, Eid prayers, and funeral processions. This indicates the desirability of walking for acts of proximity to God, provided it does not cause apparent hardship that prevents devotion or misses what is more important and beloved to Allah. Riding might be better for someone whom walking exhausts due to old age, weakness, or long distance, because Allah does not like self-torment. The reward is commensurate with the benefit and utility of the deed, not merely with hardship.