Clients who request websites have a number of options as far as writing the copy.
Some clients write the copy and the VA/web designer works the copy into the site, while other clients have the web designer do the copy and the design. And some VA webdesigners create the website and then have a web copywriter do that portion of the work.
I don't think there is anything 'typical' as I have been asked to all three or a combination of.
Some VAs are adept at doing it all and often charge one flat price to complete the entire job which includes the web copy.
There is much that has to go into creating a good website. If you feel confident enough to do it, consider doing what you can do best and then subcontracting out the other work to another VA.
Web copyrighting is much more than having good grammar. It is about creating an experience for the user while taking into consideration
SEO, good keywords, image work, and promotional copy as well.
If you don't feel confident enough to complete the whole job yourself, then consider subcontracting out the job to web designer and offer to oversee the project for the client.
Janine