Hi,
I didn't say that you need to delete all the variants of all the products. But if you only have products with one variant, that's not how it should be and that's not the purpose of the characteristics system.
If you have several variants, then yes, using characteristics is how it should be.
And regarding the issue with the price, it's because of the prices in your variants.
I don't know how you configured your variants prices as you didn't provide a screenshot of that.
Normally, you should never have any price with a value of 0 in your variants. So updating or not shouldn't change anything anyway as this situation shouldn't exist... unless the prices were wrongly added with an import of a CSV file which wasn't correct, or something like that.
Based on how the prices are configured in your variants, we might be able to provide a MySQL query to easily remove them all in one action.