We eventually had an in-house person do it and they didn't love managing it either. The hardest part of their job honestly was tracking all the ones we had, ensuring we renewed on time, and talking to the procurement department to get everything squared away. When we had to move off credit cards to more corporate billing it was a nightmare to update everything.
And even when it was all buttoned up I still had to review that list quarterly to ensure we could drop old stuff, maintain which team(s) owned what service from the technical side, etc.
Next time I'm at a bigger company I'm using you for sure.