The main physics problem I see is that Langrange points are naturally unstable [1], so the bubbles would need to be constantly correcting their orbit. This problem would be compounded by solar radiation "blowing" the bubbles back to Earth. There are clever ways to mitigate this for other designs which are addressed in the video, but I don't see it addressed in the article.
Edit: it looks like it is addressed somewhat in the source article linked in another comment, by placing the bubbles a bit further towards the sun than the L1 point to compensate for solar winds. Also, If a bubble does eventually become unstable, they may be cheap enough to destroy it and send another one up.
However, the primary problem I see with this approach is that we are simply not politically ready as a species to attempt a global-scale engineering project like that. Some countries may find that climate change actually benefits them [2], or may even impact a geopolitical rival even worse. These countries may be inclined to send a few missiles toward L1 if thats the case.
Edit: Additionally, even if this does succeed, countries may see this as an excuse to keep burning stuff despite the additional negative consequences of carbon emissions [3]
[0]: https://www.youtube.com/watch?v=G-WO-z-QuWI
[1]: https://en.wikipedia.org/wiki/Lissajous_orbit#:~:text=In%20p...
[2]: https://www.nytimes.com/interactive/2020/12/16/magazine/russ...
[3]: https://www.noaa.gov/education/resource-collections/ocean-co....