While most arcade games in the early 80's had exposed circuit boards bolted to the wall of the cabinet, many later game boards were partially or completely enclosed in metal frames or cases for various reasons...
1) protection for the boards from accidental damage while working inside the cabinet
2) shielding for RF interference
3) better cooling with fans and directed airflow paths
4) physical mounting is easier and more secure for complex multiple board configurations
Basically, the hardware got more complex and PC-like, which required better housing and mounting solutions.
I originally tried de-casing my PC and mounting it to a board inside my cabinet, but I wasn't happy with the results. The video card wasn't very stable since it sticks out of the board at a right angle, and the whole setup was hard to work on when I needed to change anything.
I eventually ended up installing a roll-out shelf in my cabinet and I installed the PC parts in a HTPC case from Antec...
http://www.newegg.com/Product/Product.aspx?Item=N82E16811129034The case only fits micro-ATX motherboards, but it can handle a full-sized ATX power supply and full-height video cards. The case is compact, but not limiting.
Note that I didn't pay that much for the case. I bought one off Ebay that had a few minor scratches (nobody ever sees it anyway inside my cabinet) and didn't have a power supply.
Now, when I need to work on the PC, I can roll the shelf out and remove the top side of the case to access everything. And if I need to do more serious work, I can easily remove the PC from the arcade cabinet completely.