Forcing people to make private ops groups just to pug a HM op sounds a bit ironic in my eyes. Puggers need a random button for all content (with ops tier and lockout progression) while manual grouping needs to be saved for people likely to meet again.
In my personal opinion, based on experience, is that a pug formed through the group finder for HM Ops is more likely to fail than it is to succeed.
The story mode ops are pretty simple. It doesn't take a lot of effort to get the group coordinated enough to pull off these encounters. A HM ops requires more coordination, a tighter level of dps and a better understanding of mechanics.
If you're not a hard-core raider, and you don't have the ops on farm already, you are could to have to work at the encounters several times before you can get through it. A pug T/Z will take several attempts just to get the tank swap mechanics smooth enough to pull it off. After several wipes people are going to get frustrated, quit and complain on the forums.
This will result in 437th threads complaining about how impossible it is to do HM Ops through the group finder, with 1,043 responses saying a) you suck or b) learn the mechanics or c) get a guild or d) yeah nerf it it's too hard.
When I first started HM EC, I had a guild and we wiped dozens of times on Toth/Zorn, racking up impressive repair bills. When we got our heads out of our *****es and actually figured out what we were doing, we were then able to progress to Firebrand/Stormcaller (surprisingly easy by comparison) and then Vorgoth. We're not hard-core server-first raiders -- but we eventually mastered that content.
But let's be realistic, you're not going to get hard-core raiders in the group finder. You're going to get the guys that need 37 attempts at T/Z before they figure it out. No pug can survive that.