Satoshi called coinbase transactions as "incentive" in bitcoin whitepaper. It is just an incentive, and it is meant to end. I see no problem, as the incentive is needed only while adoption is growing. And as adopting grows, incentive get lower (halving).
6. Incentive
By convention, the first transaction in a block is a special transaction that starts a new coin owned by the creator of the block. This adds an incentive for nodes to support the network, and provides a way to initially distribute coins into circulation, since there is no central authority to issue them. The steady addition of a constant of amount of new coins is analogous to gold miners expending resources to add gold to circulation. In our case, it is CPU time and electricity that is expended.
The incentive can also be funded with transaction fees. If the output value of a transaction is less than its input value, the difference is a transaction fee that is added to the incentive value of the block containing the transaction. Once a predetermined number of coins have entered circulation, the incentive can transition entirely to transaction fees and be completely inflation free.
In an “ideal” scenario where BTC is used on a daily basis for everyday purchases, the number of BTC TXs would increase drastically to levels very distant from the current ones, giving an edge to capitalizing on TX fees. TX fees themselves will also rise as well, and I’m pretty sure we’ll see some technological changes that facilitate all this.
I agree that we will have a drastically increase in the number of TXs, but I don't think fees will rise.
If there are too many TXs, fees can be low and even so miners get a good reward. If fees are not enough to keep mining profitable at current hash rates, miners will leave and hash rate will drop, making mining profitable again.
The system is able to auto regulate itself, and users are also part of this regulation, by choosing low fees when transactioning.