Your argument isn't supported by the turnout results. Average in 2016 was about 59%. Non-swing states like CT, DE, IA, MA, MD, ME, NJ, OR, NH posted 65%+ turnout. Many swing states did have solid turnout, but even among states with similar tight margins there's a wide variance, like 75% in MN vs 66% in MI.
Maybe you could say states that transition from being safe to swing states see a turnout boost? I haven't checked. I would expect that turnout is more determined by demographics and inertia (states with high turnout in prior elections continue to do so, etc) than whether they are swing states, though.
Edit: Data from here: https://ballotpedia.org/Voter_turnout_in_United_States_elect... (notably PA and WI are missing)
Maybe you could say states that transition from being safe to swing states see a turnout boost? I haven't checked. I would expect that turnout is more determined by demographics and inertia (states with high turnout in prior elections continue to do so, etc) than whether they are swing states, though.