This really depends upon the project and any scope definition discussion you have with the client.
I often indicate the need for a logo, specific product imagery, and a style guide (if one exists) as standard items. However I generally don't request any typefaces, even if there are specific requests for specific typefaces.
The reason I don't request fonts is due to licensing. If a client provides a font to me, then I can only use that font for that client. In order to use the font for any client, I need to own a license for the font. Therefore I prefer to go purchase font licenses myself. This removes most usage restrictions and allows me to freely use the typefaces I have without concern about who owns what.
In addition, I wish to remain legal with my software. Therefore I can't really verify or even tell if a client has the legal right to share any typefaces with me. Most clients have no clue about proper licensing and restrictions with sharing font files. And honestly, most don't care or are annoyed to discover font files are software with licenses. So they'll often simply hand over files without a second thought. But, if I'm caught with the font and no license, it's me who will end up in legal trouble for it, not the client who gave me the font.
The cost of font licenses, for me, is simply the cost of doing business and calculated properly for tax purposes. The same way I wouldn't expect any client to provide me with Photoshop to use and it's a tax deduction as part of operating expenses.
I'm not stating this is the absolute correct way to handle specific typeface requests. But it works well for me.