In reply to Offwidth:
The mechanics are pretty simple
1 The owners, if they take an interest in the paper's editorial stance, choose an editor who will reflect their chosen view
2 The editor will in turn select contributors who also reflect that view, plus perhaps the occasional dissenting voice for variety
3 Good cartoonists have a disproportionate impact because of the immediacy of their work and can perhaps set the political tone of a paper more than any other single contributor so they cannot be allowed to use the paper as their personal soapbox with no editorial control. If their stance is either seriously out of kilter with that of the editor/proprietor or that tone changes with a new editor they are liable to the chop.
(As an aside I wonder how many will scream about 'freedom of expression' if Paul Dacre's replacement at the Mail drops some of their more rabid columnists)
4 Additionally a cartoonist with a bee in their bonnet about a particular person or issue can become stale and, the biggest sin of all, boring