I tried that for a day...maybe two.
But after 5 kids and now one grandson...I gave up a LONG time ago(probably about 1989). Easier to buy a carpet cleaner and replace carpet every 20 years. If you have kids, shoes will be the LEAST of the issues that carpet sees!lol! Don't buy new furniture for about 15 years either as well. Oh..."barefoot is best" may work where you live, but not so much up here in January.
Although my Cuddy is still in great condition and I usually don't wear shoes while underway, I climb in and out of it with my flip flops on all the time. If your seats and carpet are damaged due simply to everyday soft soled footwear...time to upgrade anyhow.