The advantage of storage is that you can verify more transactions. However, that is not much good if other miners drop your block because they dropped the UTXO.
If you have 1 MB block size limit and each input is approximately 250 bytes, you only have at most 4000 inputs per block.
Thus you only have to buy hardware which can do ~400 random reads per second if you want to spend no more than 10 seconds to verify a block.
I'm fairly certain you can do this with 4 ordinary HDDs if they can do reads in parallel.
Or you can buy a SSD, pretty much any device can do more than 10000 random reads per second.
As for inputs in transactions not included in blocks, you can just drop ones you cannot fetch in a reasonable time. There is nothing wrong with dropping transactions.