But nothing actually makes you engage in the tactical combat portion of the game, either, so I'm not sure what the statement gets you.
The same thing you are getting at from the opposite direction.
Ironically, games that have extremely detailed combat rules are notorious for pushing players (in the long run) away from combat. Combat resolution in such games may be so lengthy, tedious, fiddly, and often lethal, that players are discouraged from running games with frequent combats and instead may spend a lot of time on melodrama to make the few times they do engage in combat more worth while. Conversely, rules light systems with simple fast combat rules may in fact end up being mostly about combat, since there is no great burden on the players in resolving many such small combats.
If the sheet is mostly about their combat options, the players will naturally drawn to those options.
I guess that's where I'm disagreeing then. I've played 8 hour sessions of 1e AD&D where no dice where thrown the entire session. Yet, arguably in 1e AD&D there is nothing on the average character sheet that isn't a combat option. So what happened? Why were we playing a game not supported by the rules? Arguably, because it wasn't supported by the rules.
RPing isn't really about the rules. RPing is generally a improvisational theater game that seldom and usually doesn't intersect with the wargaming inspired tactical combat game that is the modern RPG's other parent. RPing is about acting out in character in a natural manner. It's about a fantasy dialog. In fact, arguably, systems that provide heavy support for social interaction end up undermining their own intention to encourage role playing, because the resolution mechanics for the social interaction can then effectively replace the role playing. If there are detailed social interaction rules, the tendency is for the player to make a rules proposition rather than role play: "I make a Cutting Remark social attack on Sir Badwell.... 17... And that's a hit, so you temporarily reduce his reputation by 5. The Young Admirers titter in delight and now move closer to you. Sir Badwell tries respond with Cool Indifference in order to avoid improve his reputation save." That sort of rules resolution tends to turn opportunities for role play into just another sort of tactical war game.
Now, it certainly doesn't make the characters not role play. But it gives them to the option to not do so should they want to. But players and DMs that expect theatrics are going to do them regardless of what the rules support for them is.
It's funny, but the last 20 hours of my campaign the most common dice roll by far has been 'Sense Motive'. The players regularly throw Sense Motive checks to get some insight about the NPCs they are speaking to. We've spent probably 16 of the last 20 hours in theatrical RP and only 15 minutes in combat (the rest in exploration). But I've been chuckling about the fact that 95% of the time, they don't actually need to make the checks - the answers they are getting are just validating what's obvious to them from the role play. They only ask for checks when it's obvious to the player that I'm role playing the NPC as lying, and so of course, the cleric asks, "Sense Motive, is he lying?", and the answer come back, "Yes.", and the response is, "I knew it!" So they did.