fidelius charm - Why wasn't James Potter his own Secret Keeper?

Why wasn't James Potter his own Secret Keeper?

The whole thing came about because Potters chose the wrong Secret Keeper (who betrayed them) for the Fidelius Charm on their house.

Why didn't James just make himself a Secret Keeper?

We know that it’s possible from Deathly Hallows: (Bill and Arthur Weasley are their own Secret Keepers).

“I’ve been getting them all out of the Burrow,” Bill explained. “Moved them to Muriel’s. The Death Eaters know Ron’s with you now, they’re bound to target the family – don’t apologize,” he added at the sight of Harry’s expression. “It was always a matter of time, Dad’s been saying so for months. We’re the biggest blood traitor family there is.”

“How are they protected?” asked Harry.

“Fidelius Charm. Dad’s Secret-Keeper. And we’ve done it on this cottage too; I’m Secret-Keeper here."

Answer

Just my guess here, but it could be that it might be possible for the Secret Keeper to accidentally bring people into the Fidelius charm's protection.

It was seen that if someone side-along Apparates with a Secret Keeper, it is possible for him to come into the charm's field, even if the Secret Keeper didn't intend to bring him along.

We have seen that the secret can be passed by the Secret Keeper by intentionally communicating with the person he wants to share the secret to (Dumbledore writing the location of Grimmauld place to Harry) and most probably it can also be shared by direct face-to-face communication as well.

My guess is that other more indirect ways are possible. For instance, Lupin was also a Secret Keeper in the last book, just like Harry was. He said that he had to Apparate precisely onto the doorstep so as not to be seen by the guards outside. This is the same thing Harry and the others do as well when they have to leave Grimmauld place and come back. Notice that they don't just Apparate at some place just outside the field of the charm and walk inside (which would have been easier to do). Probably if anyone saw them doing that, it would be good enough as telling them the secret.

The inhabitants of a residence under the Fidelius charm will, sooner or later, need to come out of the protected area for one reason or another. If James himself was the Secret Keeper, it might have been easier to keep track of him whenever he came out of the protected area and "accidentally" get him to show the secret to someone else. But if the Secret Keeper was someone who didn't live in the house, if he made sure that he didn't go to the place himself and didn't blurt out the secret to anyone, the secret can be relatively safer.

So in short, it is less safe for the resident of a house under the Fidelius charm to be a Secret Keeper because he might accidentally show an outsider where the house is when he has to get back in.