If you mean that over time the incentive to centralization become stronger, yes, you are right. There must be competition to enter the blocks, otherwise when mining subsidy ends, there will be no incentive to secure the ledger.

If you mean that ten times the transaction have a computational cost 10 times greater (or 5, or 2), you're wrong.

> The whole point of the system is to verify transactions and it stops working if it doesn't do that.

Plenty of cryptocurrencies are mining tons of empty blocks. on the short term, if there are no transactions, mining continues with the same difficulty.

The effect is long term: if noone is using the currency for transaction, it has no value so less and less people mine it. The difficulty drops, and the security drops, pulling value down even more.

You are almost right, but it is a very indirect effect, and takes years to manifest itself.