Paying more doesn't solve anything. Under a free market economy paying more (higher demand) leads to more supply.
Not always. If the supply is inelastic, then the higher cost leads to lower demand. Eventually an equilibrium is reached where the demand that is willing to pay the cost is approximately equal to the supply that is available. Those that aren't willing to pay that cost simply stop creating any demand.
In Bitcoin world, supply (network capacity) stays the same.
Correct. Without a protocol change, the supply is inelastic. There are efforts to create an elastic supply (such as Bitcoin Unlimited), but there isn't enough demand for those changes yet for them to be implemented.
In the meantime, the demand and cost are elastic and will adjust to match the current supply. Perhaps the bitcoin blockchain will only be useful for those that are moving thousands of dollars worth of bitcoin and are therefore willing to pay tens of dollars in transaction fees?
Without increasing block size, Bitcoin network is doomed (which will force me to alt-coins). Because 3 hour Bitcoin transactions are a non-option.
3 hours for confirmations aren't necessary as long as you are willing to pay a high enough transaction fee. Bitcoin isn't "doomed". It will just become an expensive luxury, and will only be available to the elite that are willing to pay a significant transaction fee for the privilege.