[BUG] Only 40 FPS with an overclocked GTX970... REALLY????

8 is fine.

PS2 uses around 3,5GB as you say - upwards of 4GB let's say as a conservative estimate (easy to verify).
The OS itself uses around 1GB at a conservative estimate.
Any remaining RAM may get used for caching of often used files just to put the spare RAM to some use - but this is irrelevant to gaming, and for users with a decent SSD that whole function is largely redundant in terms of performance anyway.

Obviously this leaves a lot of free RAM on 8GB. Adding even more is pointless for the purposes of playing PS2 as unused RAM does nothing (except provide even more free space for the OS to try to cache stuff).

The only reasons to go to 16GB is:
- It's quite cheap...
- In some rare cases you may actually use more than 8GB. I've yet to see GAMES that actually manage to use up this much RAM, but Photoshopping print-sized images, some types of video editing, datacrunching and other niche tasks absolutely can. Any time you ACTUALLY use more RAM than you have it is well worth having, as swapping is orders of magnitude slower...

Unless you use your computer for these types of specialized work-tasks then 8GB is ample for almost all normal use-cases, and in that case you probably know if you need extra or not...

Consider getting 16GB on your next new system just to future-proof and because it's cheap, but upgrading to 16GB for PS2 is barking up the wrong tree.

There's a lot of misinformed advice on the internet...
-Stigma

As Sigma mentioned it, 16GBs or more are for photo-video editing, 3D rendering, or for strange magical stuff that some strange coding wizards do. And even for those casess, you can definitly do a lot with 8GBs only. You'll need more RAM is you're dealing with really large files.
Also keep it mind that RAM standards change too. When you'll have to get a new CPU, you'll need a new Motherboard, and maybe your "old" RAM will not be compatible with your new hardware.
Keep your money if you only go for offline-online pew-pew.