The drive *across* Ottawa is 20 minutes max at top speed. The issue is getting to the highway. I live in Morgan's Grant and have had to go to Colonel By highschool a few times, recently. Takes about a half hour, and 12 minutes of that is spent on March Road getting to the highway. Getting out of LeBreton will be similar (but worse).
CTC holds 18K and you have 4,000 cars in the parking lot, most hold 2-3 people. A few hundred more cars park around. Of the 18,000 people I'd say 12-15,000 are driving. That simply will not work in LeBreton, so mass transit will be absolutely essential, and it will not serve Kanata.
Guess you're right, no one cares about Kanata.
LRT will not help Kanata/Stittsville.