Try being barefoot more.
When you wear shoes and socks or stockings, you feet naturally sweat. This moisture makes your skin soft. But when you remove your socks or stockings, the moisture drys and then your skin can get very dry. This is probably why you find the lotion and scrubbing helpful.
If you are barefoot more, the skin on your feet can better regulate the amount of moisture in and on your feet. Over time, this should help your skin to stay at the proper moisture level. Keep using lotion and scrubbing if necessary.
Your choice of footwear may also affect the moisture level of your skin. But, without knowing what you wear, I cannot offer more tips.
I have been a 24/7 barefooter for a few years. I do not have any problems with dry skin or callouses. My feet feel like leather and the skin is tough, but still soft. You would have to feel the skin of a barefooter to really appreciate it.
Walking and running barefoot on rough surfaces like pavement and gravel and even beach sand are excellent and natural exfoliators so I never have to scrub my feet to remove calloused skin. The only scrubbing I do is to get my feet clean, not to remove rough skin. Most barefooters also use lotion, so I recommend that, too.