When I had my full PC setup up till 2012 (which I had to sell due to some feared health costs at the time) and even now on the laptop that I am using till the new build next year, PC gaming has been "cheaper" than it would have been on console regardless. However I am not focused only on the "AAA" gaming you suggest in the OP, so this might not be as relevant.
Outside the upfront £700 I spent on the original system back in 2007, I simply put aside the money that would have gone on Xbox Live, and decided to use it as a way to continually upgrade my system every 2 or 3 years, just by choice rather than necessity. Each upgrade was less than 2 years of Live, around £60 to £75 depending on what was being bought and what the original components sold for. That would have kept working to date.
As for the games, they have always been cheaper on day 1 than the consoles on the occasions that I did spend day one, whether "AAA" or otherwise. Shopping always varies depending on prices but I only shop at authorised sellers (which the OP seems to suggest is always shady, which is not the case), be it GoG, GMG, Humble, Nuuvem or even just Steam itself. Generally day one I can expect a between £10 - 20 saving over the respective console release.
However due to this, and due to the sheer wealth of games available on the platform - there is practically no reason any more to be focused on pre-orders and day 1 game buying particularly for "AAA" games due to all the season pass and dlc shit. Moreover, there is practically no reason to be so laser focused on "AAA" titles. Just due to the games alone, I'll be busy with everything from mid-tier to indie and older titles that there are simply tons of excellent content to buy that are more worthwhile to me - making it all the easier to set aside most of the "AAA" games that are quite honestly dull and monotonous to me the majority of the time, to a later date.
If you were to only focus on those, at least in the UK the result is still significantly cheaper games day 1, and due to the mechanics of the PC market - the wealth of competition and sales, the games go on sale more often than console counterparts, generally with a bigger discount, sooner, as long as you are willing to wait a little for that to start.
Ultimately if you are saying "saving with switching to PC" if you are taking the system into account and are doing something like I was, you won't see the "saving" till much later on due to the initial cost. If you are not doing as I was, you'd probably see savings a lot quicker with out Xbox Live / PS+, cheaper games (at least in the UK), but then the issue comes with what sort of system you started with and what your preferences are to upgrade moving forward. I have friends still using their original 2007 builds, using only second hand parts to keep building when they feel like it. They have definitely saved a ton.