If DMs have only 1 Skill Encounter and 5 Combat Encounters , 16% of the time you are in a Skill Encounter, 83% fighting.
Now --- same choice in front of the PCs and it is doubtful they will pick something that helps them beat a skill challenge.
I am not saying that players should be up against skill challenges half the time, but increasing the massive chasm of difference in time spent on skill challenges would encourage the players to start focusing on skills as much as their damage rolls.
The problem is not so much the % time, but the consequence of failure. You fail combat, you die, you fail skill challenge, you might lose a surge or two.
I think more skill challenges (or even just required checks) during combat (that can lead to that combat failure), might give players a reason to pay more attention to skills. If each combat has a purpose, it's not difficult to come up with skill uses during combat, terrain features, hazards, traps, or otherworldly entities are all going to be serious threats.
But even that, is not going to be sufficient if players can succeed without paying attention to their skills anyway. So ultimately, you have to create situations where the PC's fail, and when they look back at their failure to figure out what went wrong, the answer shouldn't be "we didn't deal enough damage", or "we didn't have enough healing". If the answer is "we couldn't succeed on a thievery or dungeoneering check" then, and only then is the mission accomplished, and you might have some players beginning to think about bolstering skills.
I don't know if all that effort is worth it. It might just be best to let players pick what they want to pick. Forcing skill focus down their throat is not in the best interest of "fun". But if a player does pick skill focus, I would almost feel obligated to make sure it comes into play.