An interesting read but nonetheless approaching this from asking % of cabins being Y and J, measuring square inches per seat etc, and focusing on average costs etc does not provide a good answer in my opinion.
To me the answer to this lies in considering the marginal customers and alternatives to them.

United's best customer is the customer who pays full fare J for the last available seat on a full flight. In this case, the most possible revenue has been collected.
United's worst customer is someone who paid for a deep discount business fare in a sale on a flight that goes out full, but that there was one customer who came to book their last minute full fare J. wanted to book United and had to book on another airline because United couldn't sell them a seat on that flight. Whilst United may have got 1000 USD from the one way portion of the sale J ticket, actually, they have really left 5K or more of revenue uncollected.

Every single customer flying in TATL basic economy K fares for the low prices they are today is still a good customer for United, as long as rev management have got their modelling right and don't let the flight go out without any empty seats but with customers wanting to pay full Y, W or J.

They may not be "ideal" customers, but any customer that gives United a little extra revenue such that their LHR - EWR economy cabin only goes out with 19 empty seats rather than 20 in the middle of winter will have improved the airline's profitability.