It works fine as long as you can afford the minutes all on your cell phone.
I kept my landline originally so my young daughter could call 911 easily and could get help quickly. Now that she is older, we dropped it. Other than that and not being able to send a fax, I have had no problems or concerns.
Your cell phone might not be any use to you if the power is off and/or towers are gone during some kind of weather/emergency problem, where a landline works without electricity or towers.