They had three downs to work with, with 26 seconds and one timeout. That's not enough time for three running plays.
To be fair, they had 26 seconds left because they let 30 seconds run off the clock. If they wanted to run on 2nd, 3rd, and 4th down with only one timeout, they could've done that by getting the play snapped 20 seconds earlier.
I think the smarter game-theory play for Belicheck is calling the timeout. The most likely outcome of Seattle's drive with 2nd down and goal at the one is a lead-taking touchdown. The Patriot's chance of winning is statistically more affected by having an additional 30 seconds, not the increased interception opportunity created by "forcing" Seattle to throw on one of the hypothetical 3 downs remaining.
EDIT: I do think if Belicheck calls a timeout and Carroll has 2 minutes to stand around and think about the call (and ~45 seconds on the clock at time of snap compared to ~28, he calls a run). Regardless of play call or time out strategy, Patriots obviously had a very small (football outsiders put it at 9% statistically) chance of winning going into that play and no run v pass or timeout strategy was going to significantly impact that.