I don't think Minato had large reserves. I think he had average or above average but more so hella good chakra control.
Kushina never had large reserves either she had a strong chakra. Stronger than her clan mates which Naruto inherited from her.
I don't even get the reserves discussion tbh. The anime made it clear it wasn't his chakra, it was the beast or whatever that thing is.
It has shown to give out it's chakra before, but Boruto who has a connection to it somehow with his eye, probably gave it a conduit to use his summoning jutsu to bring it out in the open.
It isn't a free power up, like you said, unless Boruto can tap into this power willingly and start summoning this thing as a pet. Which I doubt anyway since the preview kind of ties this all down to Orochimaru/Mitsuki.
It most likely gonna die, I think. Filler design vibes