I thought the dev's reasoning for not making them big/the real thing was because they didn't want so many large summons running around.
I tend to agree, with respect to the lore, it kills immersion. (Sorry, Wint!)
I see the situation being a lot like Bahamut in FFXI. No one could summon him because he was the big boss celestial avatar. Having all SMNs just call him at any given point trivializes his existence.