What is the advantage of having smaller blocks?
Smaller blocks can propagate with less latency and bandwidth and also require less resources to validate. Smaller blocks allow for more people to run full nodes as the network bandwidth requirements are lower. Larger blocks will likely lead to fewer full nodes and an increased orphan rate.
All of the data gets converted to a merkle root at a later date anyway so there shouldn't really be a size problem should there?
No, that does not happen. The section about that in the whitepaper only refers to on disk storage for which we have a much more efficient method: pruning. The network and computational requirements still exist as full blocks still need to be uploaded and downloaded and then verified.
Besides, I thought that the block size is undetermined anyway - It's up to the miners to choose how many transactions they want to put in each block.
There is a maximum block size which full nodes enforce.
Is there something in the current protocol that is stopping miners from including, let's say, 100,000 transactions in each block?
The maximum block size which has been redefined by segwit to be block weight.