I think the biggest attraction to the bean-counters is the way the new website only shows half of the fare at a time, while the old website gave you something of a teaser r/t fare that you had to play games to get to... but in any event, you had a target low fare in mind. No such animal with the new website; you don't see the totals until you've gone to a bit of trouble selecting your flights.

UA's change to giving you just half of the damages at a time isn't a new thing; Southwest & AA & JetBlue have been doing that for ages I think?

So... any armchair redesign of UA's website should probably keep in mind their strong desire to keep revealing only part of the total fare at a time. I think.