Having played 83 teams, you can count the number of times on one hand that my primary starter at shortstop wasn't a 2 or a 1. However, in a recent 60s league, my team was on the verge of fading into oblivion early in the season.
Kubek was my shortstop, and he was hitting well below .200. In desperation, I picked up Dennis Menke, ss-3 e25. I don't think Menke is a good value unless you get one of his two best years--as I said, I was desperate. I got his best year, and Menke (along with a couple of other changes) helped my team turn things around and get into the playoffs with 92 wins.
Interestingly, for much of the season, I was also playing Ken Boswell, 2b-3 e29, at second base. It was only after someone late in the season foolishly dropped Mazeroski, whom I correctly guessed was on his best season, that I had a good fielding second baseman.
So, while I agree good defense up the middle is important, don't limit yourself with absolutes--especially when you have a set of players like in the 60s where you have limited options.
Here's the team I was referring to if anyone is interested:
http://365.strat-o-matic.com/team/1441259