Hi there,
I don't think that perspective is supported by RAW. From the Summoner rules:
Lastly, the connection between you and your eidolon means you both share a single pool of Hit Points. Damage taken by either you or the eidolon reduces your Hit Points, while healing either of you recovers your Hit Points. [https://2e.aonprd.com/Classes.aspx?ID=18]
Both can take damage and healing. The only distinction is that they share a hit point pool.
Both!
What I love about Pathfinder character creation is that it doesn’t feel like either/or to me. In the games I was familiar with, there were usually only a few viable archetypes that would remain fun to play as you progressed through the levels.
Here, I don’t feel like you have to choose. Flavor supports mechanics which supports flavor back in turn. I’ve yet to come up with a concept that I couldn’t express with the normal character creation process, and I’ve never felt like there was a single “correct” build that I had to play if I didn’t want to be left behind by min/maxers at the table. I never would have seen it this way until I experienced, but crunchy tactical mechanics is the best thing that has ever happened to my role playing.