This is a thorny one, I think.
I don't think that independent councillors are a real threat to the main parties, but if public support puts them in power it might stop extremism in the form of people whose faces don't fit being deselected, so allow the main parties to represent their members and their constituents. The electorate should be able to decide who they want as mayors or MPs, and the parties have to respect that and represent their members.
OTOH, I understand that the point of a party is that it has particular views, and if a representative doesn't align with those views they pose a problem, so if the only way is to be independent, so be it. There is no saying that Independents will necessarily get in, but people should get to choose, as that's what democracy is supposed to be about.