Stardew Valley – Is There a Way to Consume Food Faster?

1) As stated in a comment, there is a community centre package that requires Gold star crops. (Parsnips/Melons/Pumpkins/Corn, 5 of each)

2) In Fall, there is a festival where you will be able to show off some quality products and gain points based on their quality, so bringing higher quality items will net your more points.

3) Other than that, higher quality food will yield higher health/energy benefits.

4) I am unsure whether a higher quality items makes a "better" gift than the same item but with a lower quality, but that would be another reason to keep some good quality items.

I mostly sell the quality stuff myself and try and keep some good ones for the Fall festival.

The max level you can obtain permanently is 10, but food buffs can push you higher. You can see your effective skill level on the skills screen.

That said, you do NOT appear to gain efficiency from levels above 10. Casting an Iridium rod costs 7 stamina anywhere between 10 and 13.

At the very least, fishing above 10 makes fish easier to catch. When I was trying to catch Legend, I spent two full in game days (I quit, rather than slept, so it was actually the same day, twice) trying to catch him without ever getting him above 75%, and only above 50% once. The third cycle, I ate a dish of the sea (+3 fishing) and caught him nearly effortlessly the first try. I quit again, tried to catch him without the food buff, failed hard, ate the food, caught him easily. Either there's a placebo effect or food buffs work above 10.