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Really excellent question anon. I absolutely hate how limiting the breeding system is, you must act like a mad scientist and bred your mons to death to create a perfect critter.
I don't have many ideas how to fix it but, maybe they could add more features?
Make special recolored mons that aren't shiny only obtainable through breeding like albino mons.
When an egg hatches, you get egg shell pieces, these egg shell pieces can change/increase IVs.
Some eggs have twin pokemon so some hatched eggs give you two mon. If they're shiny, you get two shinies?
Hmn, I will think about more ideas later.