Interests are paid on account balance every time a block is built (by anyone), so in that regard it doesn't matter how many accounts you own.
But there are other incentives to owning accounts, and specifically to centralize mining. A power vacuum will always be filled.
It is an inviolable fact of thermodynamics.
In my unpublished whitepaper, I have cited the research which has explained that economic control over
fungible (i.e. low entropy) resources invariably become power-law or exponentially distributed. Try to find an exception in nature.
Of course for non-fungible (i.e. high entropy) resources, such economic control over for example female vaginas is not centralized. (But to the extent control over humans is fungible, e.g. via debt, religion/ideology, and mass media, then control is centralized)
Now I am giving you too many hints as to how I solved the dilemma in my design.
note that existing accounts cannot be sold
Impossible to prevent selling accounts.
With that said, would it be rational for a new investor to buy minting accounts with the (sole) aim of selling their child accounts for profit?
It certainly is possible to create an asset that no one wants to buy and thus there is no point in discussing a design that will have 0 investment and security.
Sorry you can't defeat thermodynamics. You need top understand why some things remain decentralized and others don't. The key word is obviously
fungibility (or more abstractly and generatively the key fundamental is entropy).