Miners eliminate centralization.
There are various companies in India and overseas working on to provide simple and safe solution for merchants with off-blockchain transactions. I think, this is done for (1)eliminate transactions cost given to miners and (2) quick transactions facilitation. If I'm not mistaken then, Bitcoin separated from blockchain is just another virtual currency.
If this is true then, off-blockchain transactions will dependent on central authority just like VISA, Paypal, Mastercard etc. How? Lets assume, I manage to create hashcash which does not belong to original bitcoin pool and try to use it on off-blockchain economy. How are they going to verify these off blockchain transactions? I guess, single way to verify is by letting it pass through Bitcoin network. If it comes clean, then only they're valid coin else. Here, they're trying to eliminate 'verifying authority i.e. miners.' Isn't it?
When we'll be having large off-blockchain economy working and managing company would itself be centralized and need security like existing companies(VISA, Paypal etc) thereby escalating cost and risks associated.
Right back to where we started from?
Well this is a difficult question. For this you might need to dig enough to understand why bitcoin succeeded when other digital currencies failed (hint - double spends). The defining feature was "blockchain" (PoW was actually written to stop email spams). So bitcoin separated from "blockchain" is not bitcoin in any form and will be susceptible to "double spends".
Blockchain works because it stores the spend info, what you have described about central authority or verifying via the blockchain is simply "centralised blockchain" or blockhain itself. So not sure what you really mean by "off blockchain" then.
Though that said most of these companies already have a ledger (which blockchian is equal to), so their motivation to actually get on the blockchain gravy train (ie hire programmers etc to re-write their payments software) is next to impossible. Its just a pipe dream for many bitcoin/crypto enthusiasts (source: I work for a large bank writing payments software and most of the business have not heard neither care about bitcoin).
