Does one generally wear a tallis while reciting brachot at home to welcome Shabbat? If not, why not?

I didn’t grow up observant but I’m trying to increase my observance little by little. I’ve always been accustomed to reciting brachot on Friday night wearing a kippah, but without a tallis. I only wear a kippah during prayer, so this has always felt like sufficient ‘costume change.’ But I’ve recently moved from a Reform synaogogue to a Conservative one in which most people wear tallitot, and it occurred to me that maybe I should be wearing one at the principal time I’m reciting prayers in my current personal practice – when welcoming Shabbat. It seems, however, based on what I can find around the Internet, that this isn’t what’s generally done. Is that right? If so, why don’t we wear a tallis at home for this purpose? Thanks.