I purchased a case, SilverStone Technology CS382 8-Bay. Around $200-225.
Bought used parts off eBay:
Asus P8Z77-M LGA 1155 DDR3 SDRAM Desktop Motherboard $75
32GB DDR3 1333 $35
LSI 6Gbps SAS HBA 9200-81 IT Mode P20 $35
Nvidia Quadro P620 2GB GDDR5 4x mini DisplayPort $70
I have six 12tb drives (seagate exos), purchased refurb from serverpartdeals.com and had great luck with them and their support. I found that on Reddit data hoarder sub.
I run Truenas. 4 drives for primary. 2 drives for backup of the first 4. And I have a qnap 4 bay dumb raid box for a third backup with old drives I had. My paranoia but not related really to the nas.
Anyway it's possible and I enjoy what I built. Also that case is loud, get a fan controller too.
I was limited by the processor and some existing ram which basically dictated my purchases to save money.
You're completely right though, a more modern system would be similar in price and more capable.
I blew my budget on drives and a hot swap case. The rest is easy to upgrade when the time comes.