I usually give every soldier a medikit. I will probably carry on doing this until penalties for carrying too much weight are implemented.
Same here. This way everyone's chances increase. I usually split my squad into two or three people exploring different areas. Each person turns into a dedicated medic. I mean the two TU's to move the medkit from the holster to the hand are nothing especially considering the fact that after applying the patch you won't be able to shoot anyway.
The way I see it, this allows me to split into three to four small squads who have high survival rate. I don't see how that would work with a dedicated medic. Most soldiers have around 30 TU's. Heal is 20. That gives the medic about four steps range. If you use only one or two medics you greatly limit their coverage area.
In my case, everyone is a medic and everyone comes out at full health at the end of a mission. That way I buy myself at least one or two successful (no dead operatives) automatic missions. Then when I get in, most of my soldiers are banged up from the automatic AI and I hold small "healing parties" where everyone heals everyone. To be honest, when I found out that I could do that, I sold all my hospitals. X-Com had it more realistic in the terms that medkits applied immediate help on the field but never removed the injuries for after the fight and the operatives still had to recover after a field injury. But then it is a hassle to always have a healthy squad. But I digress...
I am definitely on the "everyone is a medic" side of this debate. I really don't see the usefulness of a dedicated medic.