For me, the biggest advantage of DRM-free is the fact I can take a 10 or 20 year old game and run it, without worrying that the developer is no longer supporting the game, the servers are dead, and so on. With games that require connecting to the developer's server (or a third party like Steam) to play single player, or multi player, I have no such warranty. I may hope that there are some unofficial servers or some other way to play the game after the official servers are down, but quite often this is not true. Especially with MMO games.
That's exactly why I buy DRM-free games and especially those that allow private servers. As of lately, I've been buying mostly GOG games, and those HiB bundles that include at least some DRM-free games. Usually, if a HiB bundle contains only DRM-free games, I use the default money split, while if the bundle contains some games with no DRM-free option, I'll set all money towards charity, as a sort of personal boycott. I loved it when HiB actually put pressure on developers to make their games DRM-free and Linux compatible. I don't care if they're indie or AAA (sure, many indie games are better, but I'd take a DRM-free, linux-compatible AAA game over a bad indie game), but pressuring the developers to make DRM-free and multiplatform games? That's what I loved about early HiB. Sure, my little boycott probably won't change anything, but at least makes me feel less ignorant.
Anyway, at least from my perspective, if GOG tried to strike some deal with Steam for a two-way connection that would be a nice bonus for a simple reason. Many of my friends play through Steam and it would be easier to find out who owns the same games that I do, and play them together through Steam as long as that's possible, while still being able to play the DRM-free version after the Steam version is no longer available. Sure, many people claim that Steam is not going away anytime soon, but can they GUARANTEE that in 10 or 20 years, Steam will still be around? What if the game's developer shuts down? Steam or not, as long as the multiplayer is DRM-based, this can still be a problem.
So for me it's plain simple:
I don't buy games directly on Steam. The only way they can make me buy games is either if they make them DRM-free or part of a bundle with DRM-free games, like HiB sometimes does. So far I have about ~300 games on Steam from HiB bundles and freebies, but I've never bought anything directly on Steam, or through any other reseller.
I'm happy about GoG Connect, as it gave me 6 DRM-free games that I apparently had on Steam from HiB bundles, without having them on GoG. Apparently I also had about 15 games that were already present both in my GoG collection and on Steam.
If GoG were to make the connection two-way, I'd consider the steam version a "seasonal bonus". In addition to the real game, I'm also getting a "ticket" to play the game for a while with my friends on Steam. I don't know how long it will last, but it's just a bonus to the actual game, so I don't mind if it will last just a short while before it becomes useless.
In fact, it might be enough to encourage me to buy (on GOG) some games that I wouldn't normally play, such as FPS shooters, just because many of my friends play them on Steam. Because then, whenever my friends play said games on Steam, I'd have the option to join. Without two-way GoG connect I'd just pass, because I'm not eager to buy "limited-time tickets to play a game" if I don't get the game too.
Now, I understand that my single case won't make enough of an impact on economy to turn a probably not-profitable endeavour into a profitable one. But if there were enough people with similar approach, maybe we could make it profitable for GoG to arrange a two-way connection. The problem is, it most likely wouldn't be profitable for Steam.
Sooo.... I guess not gonna happen :/