By the time 60 or 90 minutes has gone by since the last block, the mempool would be so large with fees that 100% of hashpower should be online trying to get them
Are you thinking hash power would be diverted from other places (eg BTC) to find a block with many fees?
No, this is assuming a single chain
then the hash power would have been in idle reserve?
Yes. If there were no subsidy and the mempool was empty, there wouldn't be a fee for the miner to get
