Yes, this exists now. You can ask Claude to output the document in markdown format and then convert that markdown into HTML, or ask for the output in HTML. For example, using Claude 3.7 Sonnet the following prompt outputs a vanilla HTML document:
write two paragraphs extolling the benefits to mariners of the Jones act and provide the output formatted in vanilla html
write two paragraphs extolling the benefits to mariners of the Jones act and provide the output formatted in vanilla html