As a sitting Senator that had already decided to retire it was a way for the establishment Republicans in the Senate gain favor. They knew it was likely to pass anyway, and his vote was so that they can now have favor from the Democrats in another vote

If later on Blunt was trying to get reelected for the position then during the primaries his opponents could use it to try and sway the batshit crazy lunatics who actually vote in primaries to vote for them instead

Long story short he didn't vote for it because he's suddenly had a change of heart, it was merely him playing the game for his asshole Republican buddies

Unfortunately he didn't get hit by a passing plane when dedicating the thing, so he's likely going to go become an even wealthier 'consultant' or lobbyist