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.
Sorry if some of this escapes me, but is there not some kind of "option c" wherein transaction fees scale dynamically to limit abuse? I guess this could make bitcoin unfriendly to microtransactions (one of it's finer points) and maybe easy to get around by scripting different origination addresses for each transaction if it were some kind of per-address limitation. Hmmm.
But let me better understand the current situation; Miners are already excluding transactions that are not worth their while? I assume they are doing this on the basis of fees paid? If this is the case, it would seem that removing the limit wouldn't change anything.... right? I mean, spammy transactions can already be assigned low priority and pushed into other blocks, so wouldn't that mitigate the problem all on it's own? Or is the fear that this could be abused by one of these entities spamming high fee transactions to themselves, solving the block making it "free", and thus excluding legitimate transactions? If this were the case, I don't see how a block size limit is doing anything to prevent this....