"sensible to just have my son's name on the lease"
Sensible from whose point of view? This is about risk management.
The landlord is unlikely to accept a situation where both names are on the tenancy agreement yet you only guarantee one of the individuals. He won't take the risk. Nor is it probably possible - joint tenants are jointly and severally liable for the rent money. It seems you may realise that.
If your son alone is on the agreement, he alone is responsible for the rent money. If he walks out on the property living her in situ, he is still responsibly for the payment, or you if he doesn't pay. Have you considered that scenario (risk).
If she leaves, he's still in the house, continues to pay, or you if he defaults.
What is the risk he can't afford to pay if she relationship breaks up (joint earners?)