My reasons are similar to your concerns. My biggest worry is that if my NAS appliance would fail, would the data on the drives then become inaccessible? I wanted to avoid RAID for this reason and with NAS devices RAID of one type or another was a defacto fact. I also didn't like that they were priced so high for comparably weak systems. Until I built my server, my files were stored on internal drives in my desktop and backed up on matching external drives.
As to my server. First, it was cheaper by a fair margin. For about 500 dollars, I built a low power Haswell system with 8GB of ram and onboard support for 6 SATA3 drives with space for new SATA controllers. My microatx case has room for 8 drives. Second, Linux is free and with Debian or Ubuntu Server you can do anything you want with it. Third, as per my preference I can avoid RAID entirely and mount the drives individually. Why would I want that you ask? Well, if everything but the hard drives died around it is very simple to move those drives to another system. So, if my Linux server died tomorrow, the drives can be installed and mounted on another Linux install with no array to rebuilt, just as a Windows NTFS drive can be moved around. Windows can even read EXT4 Linux partitions with the Ext2Fsd driver so if push came to shove I could still get that data off the drives. Assuming you maintain proper backups, drive failure is a non-issue, though some definitely advocate RAID for redundancy and uptime. I'm not one of those people. It always seemed to me that powering up all of the array just to retrieve one small file would just add wear and tear as well as waste electricity.
There is a learning curve though and controlling a Linux box via SSH is not as straightforward as a NAS web interface. My Linux setup is pretty simple. I use Debian Server headless with Samba for file sharing and miniDLNA for pushing media to my TV, etc. For backups, I use Beyond Compare 2 and sync the Linux drives to external drives via my Windows client.
Bottom line, it was a bit of work to learn how to use Linux and get it setup, but I'm glad I did. Before I bought my hardware, I installed Ubuntu Server on my laptop and learned everything I needed to know. I recommend you do that or perhaps run a virtual install or Live CD. You will know very quickly if it's a path you want to take.