I haven't been able to find information on this yet, so below I'm assuming miners don't do this.
Say the most recent block is solved and miner Bob finds out about it at t=0. Bob already has a pool of transactions to start hashing on. However, Bob could wait for transactions with higher tx fees to show up. If he does this, his probability of finding a block will be lower (having less time to mine), but wouldn't his potential payout be higher? If so, wouldn't there be an optimal time that Bob should wait to maximize his overall revenue? What strategy should Bob use to determine his optimal wait time?
Say Bob and Bill have similar hash rates, but Bob uses this strategy and Bill doesn't. Bob ends up using less electricity than Bill, so not only is Bob's revenue higher, Bob's profit margin should also be higher, no?
Taking this train of thought further, say Jill has twice Bob and Bill's hashing power. Will Jill's optimal wait time be longer than Bob's? In other words, if Jill can afford to wait even longer than Bob can, her payout will be even higher than Bob's. That's good news for her, especially since her electricity costs are also higher.
If every miner adopts Bob's waiting strategy, what effect would this have on confirmation times? For example, Jill will end up with transactions in her block that wouldn't be there if she didn't wait. Therefore, if Jill manages to solve her block, it will contain higher valued transactions that confirmed in a time significantly less than 10 minutes. If Bob solves his block, his set of transactions should be older than Jill's, but the tx fees in them will also be lower. Would this lead to tx fees becoming strongly correlated with confirmation times?