Why use steam instead of alcohol in Army of Darkness?

Duas razões:

Because a steam engine is less time with the materials they have on hand

e

Because the engine block is converted into a whirling blade of death (possibly because the engine was already trashed)

On the first part, Ash has on hand:

1. A book on steam power (thank you, OP)
2. Access to a working forge and blacksmith
3. Plenty of wood materials

So metal, fire, wood, someone who can craft metal and a book on steam power. He's got everything he needs for a steam engine. You could argue the realism of course, but in-universe this more or less shown to be the case.

To use alcohol to run the car, Ash should have:

1. A book on converting your car to use alcohol, the modifications aren't demanding but things like updating the carburetor is non-trivial and isn't something someone will just guess at.

At this point we have to assume that the fort does not have barrels of ethanol laying around. It is extremely unlikely that they would, alcohol at the time was generally fermented whereas ethanol would be distilled. The booze they have laying around is probably wine and beer, possibly Hidromel. It is nowhere the level of ABV and purity they'll need to run the Olds.

The only reason they might have ethanol laying around is if there is an alchemist on hand who was already tinkering with distilling. There's no evidence that I can find of that in the movie.

So now we also need:

2. Some kind of a ainda, assuming one was not at the fort it will need to be crafted. This probably about the same amount of time as building parts of the steam engine, but needs to be done before any alcohol can be distilled
3. Raw materials like wheat or sugar. There might be a farm around, the hay we see in the movie will not cut it. The wheat is going to have to be collected, etc., again before the distilling gets kicked off. Sugar is a better bet, there is probably some around a fortification like this - but probably not in large quantities.
4. And finally, and this is the problem ... time to ferment and distill. You might be lucky to have hours, it usually takes days or weeks to ferment. Course they don't care about taste, but fermenting a gas tank's worth of ethanol is time consuming. And they have to do all these other steps first.

The reason why this will take so long is a catch-22. If you start with just basic ingredients (let's say sugar and water) - you have to wait for the sugar to ferment before you have any ethanol to distill. You could, as the question suggests, start with something that has an existing level of ethanol - like the commonly found mead with ... say 10% ABV ... but now you have lot more impurities to deal with than just water. So you've got a head start, but you also have more work (and will get less volume in return). Here's a summary:

When you heat up a mixture of liquids, the more volitile components will tend to come off first. There is a bit of overlap (so it is never pure), but generally we can seperate the ethanol from the water and other impurities present. The more alcohol in the liquid, the more alcohol will be in the vapour, so multiple distillations allow us to increase the strength & purity right up to 96.5%

For fuel grade ethanol - you probably need at least 90%, and you would prefer 95%. In this modern day example it took six hours to produce one liter (that's less than a quarter gallon) of ethanol that was pure enough ... and that is using ideal ingredients. So even if we skip the fermenting step, you probably look at least 8-12 hours to distill.

And if the still explodes, they are just doing the deadites job for them. So instead of waiting for ethanol, Ash and the blacksmith get to work. And in the process, they...

...totally rip apart the car. What used to house the engine block, where that carburetor thing would have been important, now looks to have the gears to turn the whirling fan of death. The actual engine is actually now behind Ash:

So it seems in order to make the DeathCoaster deadly enough, they are probably taking out most of the important parts to keep a combustion engine running. Course this part of the answer may be causal - they created the whirling blade of death because they were putting a steam engine in the trunk. But without that whirling blade of death, Ash's Deathcoaster strategy would have been much less effective.

And they also may have done this because the original engine was trashed anyway. We don't know the specifics of the damage done - but if the carburetor cracked in the drop, it probably doesn't matter how high grade your ethanol is...

It's a solid question - but I think it would take an alternate setup where Ash had different books, and access to an alchemist as well as a blacksmith. In this case the alchemist probably would have already something approaching ethanol laying around.

Would be happy to be corrected here, but as memory serves, you can run an engine on alcohol if you make some conversions. Otherwise, the alcohol burns too damned hot and screws up the engine, dangerously so.

Also, I defy anyone to prove that an alcohol powered engine is cooler than a steam engine. And many things in the Evil Dead series were done for the sake of being cool.

Edit: I believe TVTropes would call this the Rule of Cool.