The chain on my road bike never gets dirty enough to need anything more than wiping and re-lubing.
The chain lube itself does clean. So I'll saturate a cloth with it and turn the pedals while wiping top, outsides, bottom thoroughly. I'll then use another spot to clean the derailleur pulley and any gunk built up on any cogs.
Then I apply lube to the chain, shift through all the gears a few times while spinning the cranks.
Wipe off excess.

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On my mountain bike, I just use WD-40 to clean the chain. Apply liberally and wipe clean. Instead of forcing water into crevices, you're putting a water displacer in the crevices. Dry thoroughly, lube with chain lube, run through gears, wipe excess.

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Even if I were to remove the chain completely, I'd still clean with WD-40 and a brush over a drain pan. I just don't see a need for water ever touching your drivetrain.

Do what this guy does:


But I skip the soap and water...I'd rather clean my frame with a soft cloth and a non-harsh glass cleaner personally (one that says safe on tinted windows, ie ammonia-free).

And like I said above, if it's really dirty, remove the chain entirely and clean with WD40 that way.

To each their own.