Depends on how the ownership works. If the same individuals own both google and an independent Chrome, it won't remove anything. If it's legal for google to pay firefox a half-billion a year to be the default search engine for a 5% marketshare, why wouldn't it be legal for google to pay an independent Chrome 9.5B for the same right?
The ruling I referred to above was in fact that it is not legal to purchase the default search engine as this is de-facto anti-competitive behavior for a clear monopoly (which is, itself, not illegal—sometimes products dominate markets because they're genuinely better). Interestingly this means that what they've paid out (something on the order of a hundred billion, I think, all things told) is likely the floor for whatever is necessary to remediate the anti-competitive behavior.
There's also a possibility the DOJ will fumble this and make them offer alternative engines in a more aggressive manner and fine them, which will change nothing. I think the judge indicated such, so hopefully they take this opportunity seriously.
