Once Dapps start to appear, how should an average user accept this model when he/she knows that every information eventually stored on the blockchain costs money (ether-gas)?
Why wouldn't one stick to the system we have now, write as many records as you want to the database with zero cost instead of giving away ether which one day may reach a huge amount of money in FIAT?
I think there are at least two questionable premises in your question. The first is that storing data in a database is free. That's never the case. The question is really who pays for the storage.
In some instances, you might find it valuable to pay for storage. E.g., if you are an accounting firm, you might find that it makes sense to pay to store your records electronically (it's cheaper than collecting, housing, and protecting everything in paper form). Or, to use database more loosely, you might find having memories of events to be worthwhile, so you pay for hard drive storage to store a database of your photos you've taken. (Consumer pays)
As the adage goes, if you're not paying for a product, you are the product. E.g., if you use Gmail, there is a cost to providing the storage, bandwidth, electricity, maintenance, etc. This cost is paid for by Google because they make more money selling ads and collecting data about you than they expend providing the service. (Provider pays)
In other cases, the data has little value. There is a cost to storing it, but the cost outweighs the perceived value. Then the data is lost. E.g., NASA, at the time, thought moon landing videos were less valuable than the tape they were stored on, so it erased footage of the first moon landing. (No one pays)
Sometimes, multiple stakeholders might be willing to share the cost.
The second faulty premise is that giving away a (semi-)liquid asset that may rise in price one day is a bad idea. Suppose I had two envelopes. One with 100 USD and the other with 100 kuna and let you have the contents of one envelope. Which would you pick? You'd pick the 100 USD. What if I told you that the 100 USD would be worth 1000000 kuna in three years? You'd definitely take the USD. And then you'd keep it in USD. What if I told you that 1 kuna would equal 1000000 USD in three years? You'd still pick the 100 USD. But then you'd go and take that 100 USD and buy 600 kuna with it. In both cases, my offer of an envelope is worth (at best) 100 USD now, but a potentially different amount in the future. But the future value is irrelevant as to which envelope you should pick today.
Similarly, suppose you could buy a house on the blockchain and have the property transfer recorded there at a cost of 1 ETH in transaction fees or you could pay a lawyer and a government to file the paperwork at a cost of 50000 USD. I assert that the smart thing to do is pay the fee in 1 ETH and, any time 1 ETH < 50000 USD, buy a "replacement" ether. You still come out ahead. Indeed, the fact that the cost of performing some transactions on the blockchain is lower than the alternatives makes it appealing for use in such areas. In other cases, blockchains offer capabilities that were not available before (e.g. trustless gambling as @smarx mentions or bypassing potentially corrupt intermediaries such as is being used by the UN for food aid).
There are a number of possible answers to this... essentially you're asking "What are the benefits of using a blockchain? And do those benefits outweigh the costs?"
I'll give one specific example where I think the benefits are clear. Many popular DApps today are used for gambling. For a casino DApp, the primary benefit provided by the smart contract is that it makes the DApp "trustless." The smart contract guarantees that the game is run fairly and that I will be paid if I win. Without that, I need to place my trust is the operator of the app.
Whether this benefit is worth the cost depends on how much you trust the operator of the app (or the relevant government that can enforce the rules). With a secure blockchain and a well-written smart contract, there's no need to trust anyone, and when significant amounts of money are involved, that benefit is quite substantial.
