Based on my reading about the stratum protocol, it does appear that miners are sent new work once per minute, or when a new block is found, whichever comes first.
That seems far more reasonable.
I can see this particular feature preventing pools from adopting v2.
I'm not so sure. Taking the example you gave - there is a large miner who has reached a private agreement with a third party to include their transactions for a fee paid directly to the miner. This miner is mining for Pool X, and is still sharing their block reward and other fees with Pool X, but is depriving Pool X of the additional private fee they have negotiated with the third party. If Pool X decide this isn't good enough, and stop using Stratum v2, then the miner in question can simply switch to Pool Y which is still using Stratum v2. Pool X have now lost the entirety of that miner's hash power, and with it, all the block rewards and other fees for the blocks they were mining. They will end up in a worse position than if they had just continued to allow Pool X to continue to mine with their private arrangement in place.
Any miner who has such an arrangement and wants to be able to select which transactions they include will just move to a pool which is willing to let them do that, and there will always be some pools which are willing to do that. Any pools which don't upgrade will be left behind by these miners.