What exactly is the purpose of sorceresses in the Witcher world? Why does every kingdom/king have one?

Firm bosoms...

They are extremely intelligent and learned. They also have various magical means of accomplishing things in ways that no one else can.

Also, the kingdoms want to keep the mages close at hand, lest they decide they want to seize power for themselves, like the Grandmaster.

Nah, it's the firm bosoms ;)

Political interest. You can probably got into individual motives in more detail, but essentially they formed a political group and concluded it is in their interest to offer their services to rulers of each kingdom.

If I recall, they are actually a fairly recent group. Before, individual wizards and sorceresses might well offer their services (I advise you and provide some magic, you stop people from bothering my studies) but the sorceresses got into a huff over the "men only" club and formed their own group, but bigger and better organised.

Not every sorceress agreed with this or joined. See Yennefer.

Teleport for quick messenging is mentioned, for instance.
Apart from that, I guess their experience (due to long life-span) is appreciated, they're very powerful, can read the mind of ofthers...
There's plenty of uses for wizards and sorceresses as kings' advisors, really.

But it's a matter of political treaties as well, if i remember correctly. In exchange for their services, a wizard or sorceress has to be kept close at any time and be asked for counsel. It's something, the old wizards' council of Thanedd negotiated.

And last but not least, the kings want to keep them close in order to have an eye on them - they might be a threat to their power otherwise.

They're the people who think they know everything, play world politics like it was a board game and ultimately cause nothing but strife, death and destruction for everyone. Everyone has one because a.) they're powerful and b.) they insist on being involved.

[Contemporary political comment judiciously removed.]

That's how I think of them. But when I read your title I thought it said Scorseses. Scorseses are a whole different story. -88888888888888888888888888888-

In a word....



LESBOMANCY!!!!

Win!

What are you saying? There was no "men only" club of mages. If you mean The Chapter and the Council of Mages, then also sorceresses were members of them, f.e Francesca Findabair or Philippa Eilhart.

They mostly served as advisors to kings, though, some of them were occupied with research or just worked for their own personal gain. However, some mages fought with their Nilfgaardian counterparts during the Battle of Sodden Hill, so they were also useful during wars.