The 10 year timespan is reasonable because the the coins don't become worthless after 10 years (at 6.25BTC/block), just twice more prone to a theoretical attack that is still very hard to pull off. There's plenty of time to fix the system and change the block rules for example to impose a minimal fee, thus making the "mine for fee model" sustainable.
Maintaining that bitcoins will be worth still 15$ in 6 years time (when the bonus drops to 12.5) is not actually "keeping all other things equal". It implies a major source of liquidity on the market in order to displace those miners that are currently cashing out. So I think a revenue lower bound of 1500$/hour is highly probable for the mining revenue in the next 10 years. On the other hand most of the buyers are currently motivated by hype and speculative mania, and they will be long gone if the price stays rock solid for years. This is why extrapolation for the next decades are useless, the pyramid monetary scheme will long destroy it before double spend becomes a major threat.
If Bitcoin would be well accepted and a solid economy would depend on it, frauding a few Bitcoins wouldn't stop that
Frauding a few bitcoins, once discovered, is irrefutable evidence that someone has gained ownership of the 50% hashrate underpinning the security of the system. Since that someone can launch a devastating attack at any moment, aimed not at double spending but at disruption, and the same someone can rewrite history to assign ownership of all coins to himself, informationally efficient markets will drive the price very low to counteract that possibility.
I don't see the need to do so secretly, isn't Bitcoin supposed to be 'not backed by law or goverment'?
That does not mean your trades are not subject to the law of the country where they are performed. Since bitcoins have a fair market value they are taxable and fraud will attract criminal responsibility. People have been indicted for stealing WoW gold. If you barter for a house with bitcoins and fail to deliver them the contract is void, and if you do it with intent you are committing fraud. Intent can easily be proven with your ECDSA signature on two transactions with the same source.