I do the same. The problem is at step 5: some faucets (at hotels and so on) are automatic (no touch, due to pandemic maybe). I don't have a solution for this yet.
The easiest solution I've found is to use a Zeiss lens wipe; at this stage the lens is already clean so you don't have to worry about pushing dirt around on the lens, and the alcohol on the wipe evaporates quickly and cleanly.
A better solution is to keep a clean microfiber lens cloth that never comes into contact with anything except freshly cleaned lenses to dry them. Unfortunately, for me it's tough to keep one that clean for very long.
A worse solution is just to use the relatively-clean inside of a t-shirt. All three methods have their place IMHO.
