Having two chains purporting to be the "real Bitcoin chain" will be really messy, and I think the market will avoid taking that step unless the subsidy ends up being very wrong. It could happen, though. I'd prefer to anticipate the future market as much as possible in order to avoid that.
Won't the market regulate the fee by itself and provide enough computational power in doing so?
Not really. The block subsidy is a mandatory tax on all bitcoins, whereas the transaction fee is controllable by senders.
Right now the network is paying for 50 BTC of mining per block (not counting fees). If we instead pay 25 BTC per block, then we will get less computation, and we will be that much more vulnerable to attack. The reduction in computation happens because everyone who does not make 25 BTC of profit right now is eliminated after the reduction.
If there is no subsidy, then there will need to be 500 transactions (with 0.01 fees) per minute for the network to get the same amount of computation that a 50 BTC subsidy would buy. Otherwise, the computation provided by miners will be reduced because blocks will be worth less and people will be eliminated from the market.
This entire issue may be meaningless if it turns out botnets can compete against custom hardware, since botnets have no cost and will mine for nearly any amount.