There's no reason the subscription has to be tied into DLCs. They're already separate and very merchant-dependent.
Depending on who makes and/or publishes the game, there is already (in the current market) some combination of:
1) Purchase price
2) DLCs that add more playable content
3) DLCs that basically add cheats (better weapons, more skills, powerups, etc.)
4) In-game microtransactions to speed up some part of the gameplay
5) Cosmetic add-ons
6) Full-fledged expansions
7) Deluxe editions, gold editions, yearly passes, Game of the Year editions, etc. that combine some or all of the above
Really a subscription system would just replace #1, which is for many people the largest barrier to entry anyway. It basically continues down the path towards F2P games, which personally I would love to see because now we don't really have demos anymore, and it's not easy to see how much you'd like a game before purchasing anymore. There's gameplay videos and the Steam refund system, but neither is a full substitute for a free playable demo.
In my teens and 20s I was a hardcore gamer, but now I don't have the time to try out every new AAA title and certainly don't want to pay full price for them just to maybe like it enough to play for an hour or two of Sequel Syndrome (Call of Duty/Titanfalls/Civilizations, looking at you...). If I could try all the games (or at least very many of them) for free and then only pay to enhance the ones I truly love, I would save both time and money.
And this isn't some weird experimental model either. Pioneered by OnLive and then expanded by nVidia and eventually Xbox and PSN both started doing this. In those cases, they're streamed over the Internet to you, but I'd be fine with them downloading to my machine (in chunks, encrypted and DRMed) too.
I also hope you can still buy games the "traditional" route, just for people like you, but they can coexist. Maybe $20/mo gets you 50 hours of play, split up among the games you play, and then you can also purchase any title for a full subscription + DLCs?