I'm with
@yorksrob here - a fifteen minute minimum connection time would mess up a number of existing connections - this seems like a complete over-reaction for the sake of the tiny minority of people connecting from one extreme of the station to the far side (much like the obsession on here with the handful of people travelling from one end to the other on a through service like Newcastle - Manchester Airport or Edinburgh - Plymouth or Holyhead - Cardiff).
Overnight people would find that their connection into the half hourly London service was no longer valid, meaning a wait of over half an hour, making train travel look a lot less attractive (we enthusiasts know how to read and cross-reference timetables, so we can spot when there's an "illegal" connection, but a lot of people who use online journey planners will see a wait of forty minutes at Leeds and be turned off using the train)
A new bridge from the bay platforms in the north west of Leeds station over to the TPE platforms in the south west wouldn't solve the problem of the muddle of people congregating around the area immediately inside the barriers - they wouldn't use such a bridge - it'd only be useful for the minority making connections like Harrogate to Castleford. You'd have to close the whole western throat for a while (days? weeks?) to install such a bridge over all of the lines, just for the sake of people who can't do a couple of hundred yards in ten minutes - such people exist, I'm not denying it, I have some in my family, but it really would be the tail wagging the dog. And that's assuming that there's space at the western end of platform 16 etc for a bridge to "land"!
My own suggestion would be something much simpler/ cheaper/ faster to implement - a gate at the north eastern corner of the station onto New Station Street - closer to the Brewery Tap - so that people would access the station close to the eastern footbridge over the tracks, which would circulate people a lot better inside the station and distribute people a lot better along trains (since so many people crowd around the doors closest to the western footbridge). No ticket office etc required (there's that existing facility by the current main entrance) - just one person staffing a handful of barriers - providing a much faster way of accessing the station from the Trinity direction.
Keep it simple, focus on quick wins that benefit the majority - whilst I sympathise with inform people who struggle to get from the Harrogate to Castleford platforms I don't believe that there are sufficient to warrant spending millions of pounds and temporarily closing the western side of the station to give them a facility that wouldn't solve the bigger problems in the station (the crowds around the main entrance.