Outside of paperwork for immigration, here are the other important benefits of being on lease:
- If your spouse has an argument with you, she cannot kick you out of the place since you're listed as a tenant on lease. I know this doesn't happen in happy marriages and the chances are low.
- If your spouse dies or abandons you, the landlord can kick you out of the place since you're not a tenant on agreement
- You're not building history, and without it renting in your name would be harder in the future.
It's never late to include yourself on that lease, I highly recommend it. Saving a few hundred bucks is not worth it.
Also, there's always a chance USCIS can send agents to talk to property manager / receptionist / landlord. If they don't have a clue you live there or don't have any paperwork to support that, USCIS may be skeptical you actually live there.
Not having a joint lease / mortgage is one of the little red flags that weakens your case. It's possible to get approved without it, but why making it more difficult?