Is it safe to waterlog electric motors in distilled water?
For a short time? A qualified yes. Otherwise - no. There are two problems:
galvanic corrosion between dissimilar metals,
corrosion of mild steel from oxygen dissolved/available in the cleaning fluid
#1 is not a problem as long as the fluid is ion-free. Water self-dissociates, so it is ionic all by itself. It's also an excellent solvent and will "absorb" enough metal ions from the motor that it'll become mildly conductive. And then the galvanic corrosion starts - very, very slowly. So it's best avoided.
#2 can be avoided by degassing the water, and by purging the container space above the waterline with nitrogen, so that there's no atmospheric oxygen available to dissolve in water and attack steel. Oxygen from self-dissocation of water is still available though.
Due to these two issues, water is problematic. The problems can be mitigated, but the mitigation is usually more complex than using non-water :)
It's best to keep the water ice cold to reduce its reactivity and solubility of gases in it. On the other hand, it also cleans slowly then...
Is it safe to dunk electric motors in propan-2-ol?
Yes, as long as it's dry. It won't stay dry for long if exposed to atmospheric air, since it's quite hygroscopic. Alcohols used for washing motors and such are best kept in hermetic containers purged with dry nitrogen. Then you open the container just to load the motor, close it, and re-purge.
Water can be removed from alcohol with desiccants of various kinds, and/or by bubbling dry gas through the alcohol. The alcohol needs to be condensed out of the gas. It may need to be then distilled to get rid of water before being circulated back into the cleaning tank.
Approaches to water removal really depend on the scale of what you're doing. I've dealt with bus-sized things that were washed in ethyl alcohol. Keeping that alcohol from escaping to atmosphere and usable took a lot of equipment to process it and loop it back.
Why is it safer to sop electric motors in propan-2-ol, but not distilled water?
Distilled water is not quite a misnomer, but it may as well be. As soon as you put anything into it, it will start gaining ionic impurities. It is excellent at providing oxygen to rust things, as well as catalytic help for rust to form. Pure water is slightly ionic with no impurities whatsoever; water molecules self-dissociate. While in that transient state, the dissociated products will happily bind to other things, causing corrosion. The rates and equilibriums of those sub-reactions are a whole another story (as in: don't ask me, I don't know).
Water gets in places it does not willingly come out of, such as coil windings expect rust or corrosion over time even if you think it's dry.
Yes. That's because water diffuses readily into some plastics and insulating compounds, and it can get trapped there. Removing it takes lots of time, say in dry nitrogen at as high a temperature as the motor can take. Or, instead of a gas purge, use vacuum and keep the motor hot. That will prevent the purge gas from dissolving into the plastics, as it tends to do when the plastics are hot enough...
Any residual moisture can also mix with the lubricants causing more issues down the road.
Also yes. On the other hand, alcohols tend to dissolve lubricants. If a motor has to be cleaned, it's best to explicitly remove the lubricants first with suitable solvents, then do the alcohol bath, then dry and re-lubricate.
By the time you've fully stripped the motor to get it remotely dry you could have just brushed it clean or used a vac / compressed air etc.
Stripping things down helps in drying, but I'm not depending on that too much when it comes to motors. Alcohol in dry nitrogen purge, then 100-150C dry nitrogen with a desiccator in the loop to dry it properly. It can be done in a home lab without too much trouble.