This would probably be worse. The 1 MB would include the highest fee transactions, leaving the lowest fees in the remaining 0.5 MB.
If hashing isn't constantly applied all the time then the inter-block times will expand and the difficulty will reduce. This means that a pool that decides to use all of its available hashing 100% of the time now has a distinct advantage over those who are playing nicely. This is the same problem that the "proof of idle" idea had; it only works if no-one chooses to try to exploit it (which seems very unlikely).
Say, for the sake of argument that over a nominal 10 minute period we see 10 BTC worth of transaction fees. If the mempool is empty of interesting fees at the start of a block then we might like to imagine that rational miners will power down their hashing to save energy costs until the fees are worthwhile. Let's assume, for the sake of argument, that this nominally takes 5 minutes.
After 5 minutes we go from 0% to 100% as all hashing engines switch on. The difficulty will have corrected to mean that 100% of the work will nominally happen in the next 5 minutes, but that means that a malicious miner has a 2x amplification of their nominal hashing rate to do mischief in the preceding 5 minutes.
Such a malicious miner would choose to spend their 5 minutes re-mining the previous block, but dropping some amount of the transactions from it. Let's say that they try to re-mine only 9.5 BTC out the previous 10 BTC. If they succeed then they're offering everyone else an extra 0.5 BTC (5%) if they mine on top of their re-mined block and as an incentive to orphan the original block. Rational miners would definitely choose to build on the re-mined block because they get more reward from doing so.
Of course the extra hashing that our malicious miner is doing will actually push the difficulty back up somewhat, but they're still running at an advantage over the long-term. I've also ignored some of the other security implications of the hashing amplification effects (e.g. 25% of the hash rate can end up controlling 50% of the blocks in the scenario above).
The only way I can see that this wouldn't be the case would be if there were always useful fees available to mine immediately after a block is found. If block space is kept moderately scarce then immediately a block is found then everyone will keep mining and the incentives to try to deliberately orphan the last block are dramatically reduced.