If the transaction throughput was not limited in the original design the original design was flawed. Removing the transaction limit from Bitcoin could be it's undoing.
Miners still get to decide which transactions that they want to include, and bloating blocks with too many transactions limits propagation times, which is why we even now we are seeing block sizes artificially limited. Even if there were no limit, I don't believe that miners would choose to include every transaction if it were not in their interest or if it in any way imposed a penalty on them. Furthermore, we have only two choices moving forward, both of which are just different versions of the same beast, either a) block size is limited and by necessity most transactions are pushed off the blockchain and managed by large "centralized" transaction processing companies like BitPay and Coinbase; or b) Block limits are raised and transactions of any size can be transmitted to the blockchain directly, at the expense of large "centralized" mining companies like ghash.io. Personally, I prefer the option b.
Mining is a marginal activity and always will be. As the network grows it will be in the best interest of all participants to have a functioning protocol, and large companies in the space will undoubtedly subsidize large mining operations in order to ensure that the network continues to support their other business needs. I am not worried about mining centralization.