What is the reasoning and strategy behind professional League teams taking both Sona and Taric bot lane?
Sona Taric is an incredibly strong for a couple of reasons:
The use of both support items lets the botlane be even or ahead in gold while playing defensive. If Sona Taric has lane control they'll be very far ahead as Taric can get all the CS, share some with Targons and Sona will be collecting as much or more from Kleptomancy and the Frostfang line.
More importantly, late game both champions have incredible sustain. Two Taric heals and a Sona heal will bring someone from nearly dead to full. The only option is to all in the team in an attempt to get kill but Taric ultimate makes that impossible.
The speed from Sona's E and Taric support items and his proxy stun mean any team comp can just ran at the enemy in a death ball, be immune from Taric's heals and ultimate and Sona's shield and faster than the enemy. If the enemy team tries to split push they can pick someone off even under tower. If the enemy team tries to 5v5 Sona+Taric they'll be at a disadvantage as Crescendo and Cosmic Radiance are some of the strongest 5v5 ultimates in the game.
As you asked specifically for pro play, in pro play this combo is almost always paired with a Kindred, to ensure that you CAN'T kill them with the initial burst, and the heals will be very effective after her ult (which gives enough time to channel Cosmic Radiance). One of the teams in the MSI play ins ran this team with Kayle top, abusing the invulnerability mechanics to the max.
Some teams tried to play with Morgana mid to make someone trully invulnerable to both CC and Damage, but for the most part that seemed to lack enough damage to actually win teamfights in the late game.
In short, Sona Taric provides a lot of healing and durability to the entire team with Area of Effect shields, heals and invulnerability, as well as a speed buff. It also encourages death ball strategies that maximize the effect of Sona's abilities, which are quite effective with a short cooldown.