It's hard to say whether you would be "better off"...
You are renting the equipment from Cox. Those rental fees add up over time. So much so that over the course of two and more years, you could have paid for your own equipment several times over. However, Cox will support the rental equipment. Consider the rental fee as paying for tech support every month.
I've been a Cox internet subscriber for 15+ years. In that time, I've purchased two cable modems and two wireless router systems. It's straight forward to see how much money I've saved purchasing my own equipment instead of paying rental fees.
In the end it comes down to what is valuable to you. I certainly won't judge anyone who says, "I don't know this stuff. I don't want to think about it. It should just work." The rental fees might be worth it.
I do wonder why Cox rents the modem/router but makes you purchase the pod extenders... if needed, one would think the pods would be part of the equipment and included in the rental fee.... either way, you can buy these pods on eBay for $50-60. Caveat emptor.
As for your "dead" room.. there are many variables why wireless signals won't penetrate into a room. The construction of your walls, ceilings, and size of your home are a significant factor in your router's wifi signal range. As bruce mentioned earlier, purchasing your own router, one with a stronger wireless radio, could help.