You charge your laptop everyday. So it depends on how often you recharge them, which means it will depend on how big of a battery you'll buy. If you buy a 100 KWh battery (probably around $10,000-$15,000), I think that should last most Americans at least several nights to a week? So it might approach 10 years before it starts degrading, and then probably a few more years of charging it every day. I assume's Tesla's batteries will be relatively high-quality as well.
Isn't the idea that you keep it topped of and use it when grid power is expensive or missing? That usage pattern would involve multiple charge cycles, perhaps even 365 in a year. I guess it would actually follow the Tesla charging patterns fairly close as well. What is the estimated lifetime of a Tesla's battery?
If the battery has sufficient excess capacity, you can split it into multiple banks of smaller batteries, and cycle which ones you charge and which ones you use. Add a small computer and you can use whatever logic gives you optimal charging/discharge patterns to optimise for lifetime.