If you're on the fence about Urban's successor, then allow me to plead my long and convoluted case as to why he's the right man for the job.

3. Excellent offensive mind and QB coach.

Legend has it, Don Brown only ventures outside when the moon and stars cover the night sky, because he's too terrified of Day.
When Day was first hired as the QB coach and Co-coordinator after the 2016 season, many people were skeptical about him, considering he wasn't a household name, and when you looked as it résumé, it wasn't exactly eye opening. He'd been the OC at Boston College for two seasons when their QBs were most notable for handing the ball off to Andre Williams during his 2,000 yard rushing season in 2013; before being the QB coach for Chip Kelly in the NFL, where he helped tool some juggernaut QBs like Sam Bradford, Mark Sanchez, Colin Kaepernick, and Blaine Gabbert.
Those that weren't fans of the Day hire pointed to this as their concern. After the disastrous Tim Beck era of QB sweeps and 40% completion percentages, none of us wanted to see a repeat. But as we now know, Day's the anthesis of Beck. Although J.T. Barrett didn't light the world on fire with his weenie arm, he certainly improved under Day's tutelage during his senior year. And of course, Dwayne Haskins has shattered every OSU and B1G passing record during his Heisman-worthy 2018 campaign. Plus, he put 62 points on the previously #1 defense in the land just a couple weeks ago.
So while Day may not be a household name as a head coach, he really wasn't a household name as an OC or QB coach before his arrival in Columbus either.

2. Great recruiter.

While it's unknown whether Day will have the same profound impact on the recruiting ground as Meyer, during the limited time he's been in Columbus, I'd say he's off to a phenomenal start. You ever play NCAA Football, and find that 3-star gem while recruiting fictional video game characters? Well that's practically what Day did when discovering Chris Olave. Olave, according to 247sports, was the 68th ranked receiver nationally in the 2018 class, yet he's had a resounding impact on the field, catching three touchdowns and blocking a punt in just the past two games alone. I compare Olave to Darron Lee, in that Lee was also an overlooked prospect that was found by Luke Fickell, akin to Olave being discovered by Day. It remains to be seen how impactful fellow recruits like Tate Martell, Matthew Baldwin, Master Teague III, etc. will be, but I say keep the faith.

1. Continuity.

By not making an outside hire, it's expected that many of the assistants already on staff, such as Tony Alford, Brian Hartline, and Larry Johnson will remain with the team. Day's already demonstrated his desire to keep the core of the staff by retaining Mickey Marotti and Mark Pantoni. This, I believe, is just as important as naming Day as Urban's replacement. To those that wanted Matt Campbell, I say if he got the job, then you could say goodbye to almost all the assistant coaches. Practically anytime you see a head coaching change, it isn't just the head man that's new, it's nearly the entire staff. When Urban was hired in 2012, the only coach he kept from the previous staff was Fickell, and even that wasn't necessarily a guarantee. Another example would be Penn State. James Franklin was hired on January 11th, 2014 to succeed Bill O'Brien, four days later, Larry Johnson is poached by Meyer. That alone should tell you the severity of a head coaching change via an outside hire.
Now there will almost certainly be some changes to the staff. Bill Davis will hopefully be replaced, Greg Studrawa may be seeking a new home, and Greg Schiano and Kevin Wilson could be head coaches elsewhere soon. But the fact of the matter is that Day will likely keep a majority of the coaching staff together (yes, including Alex Grinch and Taver Johnson), and also keep the current 2019 recruiting class. Again, an outside hire would also mean that the new coach would pull scholarships from those already offered, and offer them to prospects that they covet.
And most especially, continuity also means keeping the win streak versus Michigan alive and well.

Honorable mentions:

Day has the greatest win percentage in history.

For all you stat freaks, you can't argue with a 100.00 win percentage.

Day's dance moves.

Ladies, try not to faint.