Will IOTA work as promized?

Currently, a lot of people made money by investing into Bitcoin and Ethereum. As a result the transaction fees for both are at the moment high enough to make most use-cases of the technology that existed two years ago impossible.

IOTA promizes to be a digital currency without transaction costs.

IOTA promizes to be able to deal without transaction costs by using a complicated concept called the Tangle. I have a hard time myself thinking through their framework. If the total transaction volumne is high enough that the whole transaction log spands multiple terabytes and nobody is incentivized to hold all that data to make transactions, does IOTA still work or will that make the system crash?

Is there anyone in this community who looked more into the concept and has a good idea of whether IOTA can till with terabytes (or even petabytes) worth in total transaction data?