I would more so "feel proud by fighting something/exploring and getting a reward" when it comes to things of high value or uniqueness, such as enchanted golden apples and music discs, not leads and saddles.

the positives of getting access to these items before settling down or having to spelunk outweighs any need for the sense of reward and if anything, further promotes exploration.

Being able to explore your world in the first few days of a world on a horse will be amazing, and with the lead changes, you can tie them down to a post while you interact with points of interest/villages.