Towers were never good. What you remember is slightly different, but it highlights a real issue.

When you reminisce for the good old days when towers were useful for something other than vision and cheap teleports, what you are actually remembering is a time when if your opponent(s) wanted to dive you, they had to walk in, start hitting you, fight you, eventually kill you, then walk out. This put them at risk.

What happens today is that they dash in, kill you 70-0 instantly, then blink back out, taking maybe one tower shot.

Towers have always sucked. Mobility creep in this game, however, is better described as mobility leap. THAT is the problem, and THAT is what Riot should be tasked with addressing.

Solutions?

For starters, champions mid-dash who are hit with snares and the like should stop instantly, rather than completing their dash first (wasting cc time, and also probably killing you anyway). Reacting in time should be rewarded. Jumps with weird trajectories such as Tristana's should drop them to the "ground" appropriately.

Movement slows slow movement. It holds that movement slows should slow movement abilities. If Riven (for instance) is under a 30% slow, her Q animations finish 30% slower. Also, damage happens at the end of the animation, as you would expect. This opens up counterplay by allowing the player to use their slow to actually dodge the deluge of hypermobile champions currently warping the game. As it is, slow fields and effects are mostly inconsequential.

Lastly, when Riot says that champions pay for their mobility, they should actually mean it. Evelynn pays for her stealth. Mobile champs pay nothing for their mobility (quite often literally).