Each time you remove point and click hard cc (Sion's old stun, Talon's silence, Soraka's silence, etc) you essentially buff mobility
This isn't really true.
Point-click mostly has the advantage of precision in large-scale fights where a skillshot would either collide with minions or unfavorable champions. That isn't exactly mobility-exclusive power.
It's very much worth noting most skillshots have around double the range of point-click effects as well. While you're not going to miss a point-click skill in the ~600 range it gives you to work with, there's no realistic downside to missing a 900+ range skillshot CC. It's a 0 risk, potential reward scenario. For a lack of reliability - you get greater safety, greater catch range, and all around better potential with skilled usage when it comes to abilities that can miss.
Also - Skillshots have a significant edge when being chased, as you can be further than 1000 range from an opponent and hit them with a 1000 max-range skill due to them moving towards you while it's traveling through the air. The opposite is technically true with point-click vs. fleeing targets, but the near double range of skillshots pretty much erases any advantage you'd get there.
Furthermore - point-click stuff has other significant drawbacks besides short range. You also can't target units in fog of war, brush, or stealth. Such effects make an opponent immune to point-click.
On top of that - several mobility skills just cannot be easily used to dodge skills. Many mobility skills are point-click and can only be used with a nearby target, many mobility skills have long cooldowns and high mana costs, and many mobility skills don't carry units far enough, fast enough, to reliably offset what decently aimed skillshots can do. Mobility as a whole doesn't counter skillshots, only low-CD, low-cost mobility tends to provide serious issues.
Finally - if a mobile target is thinking about leaping onto a squishy ally, with skillshots you can lob CC at them to catch them mid-dash even if they're out of your range, where with point-click you have to wait until the enemy lept, spending valuable time performing your CC casting animation (which is usually very lengthy for point-click CC skills) while an opponent is doing their QWER on your buddy.
Anyways - no, point click CC isn't countering mobility in any meaningful way, and it doesn't hold any noteworthy advantage over mobility.