That would require a constitutional amendment to overturn 30 years of legal precedent that gives an enormous advantage to the wealthy and connected. It is illegal for Congress to put everyone on the same playing field and disallow wealthy candidates from self funding. So any public financing would simply give an enormous advantage to wealthy candidates and dark money groups with the resources to overwhelm the publicly financed guys.

Right now in order to compete you must fundraise constantly or risk not having funds to counter the spin of a bankrolled opponent. It would be interesting if the Supreme Court simply eliminated the contribution limits but this would give even more of an incentive for congressmen simply to sell their votes("Vote for us and we will give you X gazillion dollars over four years vote against us and we drop millions in dark money against you and fund your opponents").

No, just cap the spending and maximum donation.

The 1st Amendment would need to be dramatically modified to make significant change in campaign financing.