Depending on what your lenses are made of, and if you have fragile coatings on them, and if you live around or work with fine abrasives, this works fine.

I miss actual glass, uncoated lenses.

Not missing them at all. In fact, wouldn't wear them even if I'm being paid to be that. Stone age tech :)

Grease is not entirely caught by cloth; the stickier/large the grease patch, the more it will spread over the lens, making it time consuming to clean.

My lenses have oleophobic coating. I find breathing on them and rubbing with microfiber cloth to be quite effective even when they are coated with grease.

Try running them through a soap cleaning once. You might be surprised at how much cleaner they'll end up looking after (been there with my spouse!).