I would love to see some analytics on fielding performance on batted balls in play behind strikeout pitchers as compared to pitch to contact guys.My guess would be that fielders perform better when batters see fewer pitches.Nothing like a 8 or 9 pitch at bat to put fielders on their heels.
I'm taking the second half of your post separately as I see it as a separate (and interesting) issue.
Baseball-reference.com has all kinds of seasonal stats that one can sort on. The stats that apply here would be SO/9, BABIP (BA on Balls In Play), and Pitches/PA. (Actually I wish they offered SO/PA, but it is what it is.) BABIP would seem to address what you are asking about.
Unfortunately the site does not place these three on the same page with each other, and I am not a wizard with databases. So all I can do is sort on one stat or another, and do a bit of sampling rather than try to do something more statistical. Maybe somebody with mad skillz can help me out here.
One initial observation is that BABIP is renowned for high variability. The same pitcher may have consecutive seasons of BABIP above and below average (which usually is around .300) - few pitchers are really consistent year to year, suggesting that low or high is not a repeatable skill held by the pitcher.
OK, so if I sort 2017 MLB pitchers who had enough innings to qualify for the ERA title, I see at the top for pitches per PA Jake Odorizzi. Your surmise would be that his fielders are on their heels; instead, he has a very stellar BABIP of .228 this year, indicating his fielders were making the plays for him, when the batter did finally put the ball in play. I bet he doesn't repeat that feat next year, but anyway we're off to a bad start. Next on the list is Eduardo Rodriguez; his BABIP is .300, a very average figure. Third is Wade Miley, and his BABIP is .333, in keeping with your surmise. Next is Trevor Bauer, and his is .338. Next is the sainted Mike Pelfrey, and his BABIP is .276. A very mixed bag.
Working next from the bottom of that list, the fewest pitches per PA belonged to Iván Nova. His BABIP was .303. Next best was Big Sexy himself, Bartolo Colon. His BABIP was not very good, .335. Next comes Clayton Richard with BABIP .354, Mike Leake with .312, and Luis Perdomo with .327. These are the guys whose fielders should be the most alert, and again it's a mixed bag or even trending the wrong way.
Now, this methodology, if you can even call it that, of the 5 top and 5 bottom, is slanted toward good starting pitchers - pitchers who were trusted enough to rack up a lot of innings pitched by br-com's cutoff for rate stats. Maybe a careful study that includes relievers and/or bad starters would show a different trend.
You can approach it differently, by sorting on SO/9 (since SO is the subject here), since the top Pitch/PA is not necessarily the top strikeout pitchers. Again, we'll only look at pretty good starters this way. Chris Sale was the top pitcher for strikeout rate, and his fielders allowed him to amass a BABIP of .303. Next was Robbie Ray, and he had BABIP .270. Max Scherzer, .248. Corey Kluber, .268. Chris Archer, .325.
Among the pitchers with lowest strikeout rates: Ty Blach, .296. Andrew Cashner, .267. Jeremy Hellickson, .248. Martin Perez, .330. Zach Davies, .306.
Every time I start to see a pattern emerge, another datapoint comes along to break it up. It reminds me of flipping coins.
Interestingly, as a side note, the list of highest strikeout pitchers does not correspond to the list of pitchers with highest pitcher per plate appearance. (Edit: just as Chief expressed.)
I wrote this rather stream-of-consciousness, expecting to rewrite it or at least condense it when a pattern emerged. It didn't, so for whatever it's worth, this is a very shallow but non-cherry-picked look at your question. I don't think a pattern exists, and this sampling of data doesn't motivate me to go take a course in database analysis to try to dig one out.