A half-halt is nothing more than a pause asking your horse to collect up again.. it works hand in hand with normal collection. Keep in mind that COLLECTION and HEADSET are not the same thing.
Collection refers to a horse working through itself, flexing its abdominals, rounding its back, working off the haunches, and having a stride that doesn't cover as much ground as with a working gait.
Headset just refers to the head being in a frame. It does NOT necessarily mean that the horse is collected. The horse can still be strung out and not working under himself, and have a nice headset.
With a half-halt, just think "pause" with all your aids for a split second; sit deep and tall, check with your reins, and ask for a halt with your aids... now before the horse halts, ask him to carry on in the gait you were in. There should be no break in gait. It's a simple motion that works well to get the horse working with you again, much like collecting up around your corners.
As Tim said, there are no cons to collection...when it's done right. You should not lose your half halts due to collection, it just means you perhaps aren't clear in your aids.
Edited to add:
the consequence of gaining collection is losing my half halts! And my once slow-loving horse likes to rush things now! Especially his trot!
This makes me think you're confusing collection and headset.
As I said before, collection is where the horse takes a stride that does not cover as much ground as a working gait. It should not be slower, but shorter. This means the horse should NOT be rushing at all. Once you achieve collection, you should be able to influence how long the horse's stride is, and should be able to shorten and lengthen it no problem... which is something to work towards.