My grandparents obits were in Illinois papers but we wrote them, the funetal home just arranged for publication.
The advantage to having the funeral home handle this is that they know what the local newspaper allows and doesn't, and the cost per line, etc. They can make helpful suggestions in composing an obit.
Some newspapers have rigid rules about obituaries (content, length). Others will let you write whatever you want, as long as you pay for it.
We were surprised when my father died that his hometown newspaper had strict guidelines for obituaries. They were formal, brief, you could list occupation and education, and next of kin (but not an endless list of survivors). You could not mention everyone who predeceased him, except a spouse. This is a very well-known and respected newspaper, but they keep a tight rein on things.
Where we live, the local newspaper allows very long obits. They make interesting reading, actually.