They legally could. For years. They didn’t.
My point is that government regulation is likely to make costs go up, not down, and cause a certain amount of technological lock-in as well. The history of Title II regulation of the circuit switched telephone network is an excellent example of this, and is why the FCC promises to exercise a "light touch" here.
The last two times net neutrality was in the news (during the initial reclassification, and then the repeal), the main claim then was that it would/did reduce investments and innovation, and that was a lie[0][1][2][3]. So, knowing this, what are the actual risks you see today in treating ISPs as common carriers?
[0] https://arstechnica.com/tech-policy/2018/02/sorry-fcc-charte...
[1] https://arstechnica.com/tech-policy/2018/12/attverizon-lobby...
[2] https://www.wired.com/story/the-fcc-says-net-neutrality-crip...
[3] https://www.investopedia.com/insights/does-net-neutrality-st...
As an example, as long as a customer has access to a public option for comparable internet service, private companies would be exempt from "net neutrality" regulation and penalties.