Be aggressive. Force contact on your terms with high-quality strikes and pitch away from contact after getting ahead in the count. That doesn't mean throwing obvious Balls, of course. Throw pitches that look like Strikes, but are actually borderline pitches the hitter has to protect against. That's a good theory. The bad theory ("invite contact" a.k.a "pitch to contact) is this:
It was decided that the Reds pitchers would pitch to create contact in 2004, rather than trying to miss the bats of opposing hitters. "We decided we would try to get to contact as early as we could in the (ball-strike) count," O'Brien recalled Monday.
Focus on throwing strikes. Focus on prompting opposing hitters to put the ball in play, and trusting the Reds' defense to make plays. Focus on decreasing pitch counts from inning to inning, enabling the starters to work deeper into games. The best pitchers on the staff, then, would throw more innings, while the middle relievers -- usually the soft underbelly of most pitching staffs -- would have a lightened workload.
That's just a dumb pitching philosophy- particularly if you have a bad defense and don't have pitchers who can miss bats.
The key problem with "pitch to contact" is that pitchers can't control their BABIP; meaning that focusing on bringing the fielders into play isn't necessarily going to decrease pitcher workload due to the probable increase in Innings extended due to more baserunners. Sure a pitcher might be able to cut down his P/PA by "inviting contact", but that's pointless if the practice results in more batters faced. As you mentioned, that doesn't mean a pitcher should avoid contact at all costs, but if the primary focus is on ending PA in the first three or four pitches, you've got yourself a problem.
Lastly, only the most precise pitchers in the game are going to be able to hold down their HR totals while "inviting contact".
Fewer Walks and more Home Runs? Sure. Fewer baserunners? Not likely. Fewer Strikeouts? Almost definitely. The Reds tried this crap in 2004 and 2005 and were pummelled.