OK, great, we can get something to Alpha Centauri with a lightsail. Now what?
Unless you are sending a lightsail "ark" full of settlers to Alpha Centauri, what is the point of this trip? You've just spent billions of $ to build your spaceship, sail and lasers, and you aren't getting anything back.
This effort might be worth it, if you could send a space probe to reconnoiter the Alpha Centauri system, find anything interesting, and then return to Earth. I VERY MUCH doubt that your probe would have powerful enough communications array to send any real telemetry back to Earth from 4 light years away. Plus your probe would need an ion engine or something else on top of the light sail to navigate within the Alpha Centauri system to find these interesting bits we are looking for.
So it would need to deploy its light sail, spend 30 years getting to Alpha Centauri, take down its light sail, cruise around Alpha Centauri conducting research for several years or more, deploy its lightsail again and return to Earth and then slow down enough again to be recovered, so the data can be analyzed. So on top of the engineering challenges inherent in all that, we are talking about a 70 year+ mission.
If you can't do all that, then you are not getting anything out of the mission other than a proof of concept that you can shoot something out of the Solar System using a lightsail. Humanity would be better off using that money for missions within or on the edges of our solar system.