Disposable corn plastic mesh you can lay across bottom of the sink, that works for a few washes and then dissolves, composts, so you can just compost it after each wash. As these technologies get cheaper, I think there is a definite market and it would be feasible, and it is a novel approach.
Enzymes you use to clean your sink and drain that eat the common stuff in drains, breaks down hair, body fluids, toothpaste, etc. Drain cleaners like it exist, but it would be nice to have something you used on a daily basis or something when you wanted to keep the drain from building up gunk. It already has a market, but it would be a modification, and I think it is feasible, it just requires research and a change in intensity of the current product.
Similar to a disposal, it would be great if when you closed the drain, you could pull rotating blades (like an electronic shaver) up to the drain to shave any hair into super small pieces. I don't think this is super feasible, but it is novel, but probably too dangerous to market, except people spend lots of money to rid drains of hair, and it's not less dangerous than a disposal.
I really want a pet monster who lives under my sink and eats my compost, and anything else I put in the drain. Not sure if that is an idea, except it could be, for a geneticist. Feasible, no. Novel (except the Flintstones movie). Marketable, definitely.
Use something like a flow-bee to suck stuff out of the drain. Feasible/novel--there is a flow-bee, but it would have to be like an attachment for a wet-dry vac. That might be more feasible. I believe that's marketable, especially as an attachment. Those are two ideas: flow-bee and attachment.
A flat screen that is not inverted, kind of like a diffuser on a gas range, would be a simple way to alter the often rounded or divoted drain protector. It's not super novel (alteration), but would be feasible and easy to market.