There's different systems but it comes down to trust and communication. Some players have bad shoulders and would rather defer. Others don't move well. There's also those that feel their nerves.
In general, the player w/ sore shoulders or weak overheads can keep it in play but not put it away. It's more important for you then to call it if you want it. Sometimes as a team it's easy to end up out of position since he'll move over to the side giving you space to hit the overhead. But since you've moved over there's a good window for the opponents if your shot isn't well hit.
If your partner's mobility is limited, you can't close to the net as much are going to have to be ready to move. More than likely, you will have let the ball bounce when it crosses and hope to hit a deep lob. Since you're doing all the work, your partner needs to at least shuffle over. If he can't or forgets to do this or if your lobs are landing too short, then maybe he should stay in the baseline.
The nervous player is the hardest to deal with as at one time we are all nervous and have missed big juicy overheads. I try to be encouraging and sincere in my exhortations. But I think as the score becomes more criticial, you may treat them as the "weak overhead" partner and take more overheads from them... but this is hard on teammates/relationship. Perhaps he fears you don't trust him to take the shot? Perhaps he's glad you took it and if you missed he can blame you (and not himself?)
BTW, after playing w/ partners like these it feels amazingly good to play w/ someone who can put it away without the drama. Here you both have to agree on a system. As you play more, you'll get a feel for eachother's limitations and won't necessarily need your partner to call mine or yours. Initially though that communication is essential.