This could work. A while back when someone suggested it, it seemed like a good idea.
But more recently, all of my attempts to pug a tank position in a HM Ops fell apart. The only times my HM ops have gone smoothly is when I'm with tanks I know and we pug the dps or healer spot.
I fear that if Bioware implemented HM Ops in the group finder (even with your solution above) it would result in many angry people complaining, resulting in nerfs, which imo would be worse than the angry people that are currently forced to build up a friends list to do HM Ops (or join a guild).
Then they could add a pop up warning that the content is (obviously) more challenging than the standard content. They are called hard modes for a reason, they are meant to be a challenge.. a grind to get to the top.
Problem is everyone expects to fly through them without effort, I've seen people rage quit after one wipe even though the boss was down to the last 7k or so. For premade non-pug ops fair enough you should get a goal of not wiping often but if you join a pug group you shouldn't expect to fly through content and be prepared for a few wipes.
You can't really force people to join guilds they don't want to or manually put together a group just to play through the extra content.
IMO the content should be available for anyone of that level, premade group or automatic via group finder (with a sensible progression system in place also).