Substitute actual vodka for storebought vanilla extract

No, vodka is nothing like vanilla extract.

Unfortunately the premise of your question is wrong. The thing that makes "true" vanilla extract true/pure/real is that it's made from real vanilla beans, as opposed to artificial flavors. Artificial vanilla is often just vanillin, one of the key flavor components, and it's been manufactured from another base ingredient (probably lignin), with no vanilla involved.

In both cases, the exact source of the alcohol isn't important, it's just that it's alcohol (ethanol) and water. I've mainly heard of using vodka for homemade vanilla extract, because as far as readily available liquor goes, it's about the closest you can get to pure, flavorless ethanol/water. It's hard to imagine that mass-produced commercial vanilla bothers insisting on vodka in particular.

Anyway, flavors. Artificial and real vanilla extract are really pretty similar, which is kind of the point. If you can't easily get the real stuff, or it's too expensive, there's absolutely nothing wrong with using artificial.

In particular, for baked goods, artificial is totally fine. The heat means you lose a lot of the flavor complexity, and the two end up indistinguishable, or close to it. Notably, America's Test Kitchen has done vanilla taste tests and says "It matters not a whit whether you use real or imitation vanilla, because you can’t tell the difference when you bake."

The difference is much more noticeable in things like icing/frosting, pudding, and ice cream, where you don't use much if any heat after adding the vanilla, so the complex flavors remain. So if you're making any of that, and you want it extra good, that's when you may want to splurge for real vanilla extract, or vanilla beans.

I think the idea of the vodka is that it is an almost tasteless alcohol solution which is good for two reasons. In the quantities added it would likely evaporate or remain in very small amounts and that the aromatics in the vanilla would dissolve in it.

Considering there's other forms of vanilla (including alcohol free or powdered) varients, and how vanilla is a pretty integral part of the flavour of cookies, you might as well leave the alcohol out

Your assumption is totally wrong. Putting several vanilla beans in vodka and soaking makes excellent vanilla extract ( the remainder my 1.75L is a couple years old). When I use it the alcohol evaporates immediately and I have never detected any residual alcohol. Don't know about "bitterness" in vanilla.

All vanilla extract will contain alcohol. Either whole beans are steeped in alcohol, or manufactured vanillin is dissolved in alcohol. Alcohol alone has no flavor, but vanilla extract tastes like vanilla. If you want vanilla flavor, you will need to add vanilla extract. One use of vodka in cooking though, is to allow pie crust to be wetted so it can be mixed and stay flakey without becoming bready.

If you want to make a sweeter vanilla extract, I have done this by making my extract with brandy, and /or rum rather than the vodka. I found this adds depth to the flavor. If you want to stick with vodka, try using a better one, that does not have the bitterness. Sometimes the bitterness can be taken out using a charcoal filter, like that used to remove impurities from water (see this article for details)

But as the others said, the alcohol (or some type of organic solution) is required, to allow the vanilla to be transported. The main reason for alcohol, is that it mostly evaporates off at temperatures where vanilla is commonly used.

Good Luck!