When did words like beseech, plead and beg fall out of casual use? Pleading and begging, we still use, but they are mostly only used in the most extreme circumstances. Pleading and begging turn up in violent situations and in court but we don’t go around pleading and begging when chatting with our friends. And we certainly don’t beseech them.
Rarely, we might hear an “I beg your pardon” but even that has fallen out of favor. My grandmother said it quite often – but I only ever use it with mock horrified gentility.