If I continue to install all the patches, is there really any need to update my Magento version?
My store is small and I'm not lacking for anything in terms of features, and not wanting the stress of updating... is this a wise approach?
Magento 1 will not be receiving anymore feature updates, and will only be receiving security updates for the next few years.
It is always best practice to make sure you are on the latest version, however in your case you are probably well enough off on 1.7 provided that you regularly check for modified files, logs, and keep the patches up to date.
With Magento 2, I would suggest you start taking a look at it, not for something immediate, however for something to migrate to down the road.