Whilst the chord itself is still largely undeveloped, it still has a considerable climb up towards Laisterdyke and even with some of the line straightening you suggest the route to Leeds still passes through quite a densely populated area with an already large number of services operating across the existing alignment. I'm not really sure that there would be much improvement in times routing this way with a Bradford Parkway compared to using the existing North TP route.
Old Yard Dog has touched on the issue, and I will expand a bit. Whilst Bradford is never going to compete with Leeds in terms of retail & finance, the current vision for the city is one focused more around leisure and tourism so having a central station will be key to developing these. Lots of new projects in the city are centred around the leisure industry, with a view to getting people into the city from surrounding areas for this. Plus a lot of people do commute to Leeds, the vast majority of these would not benefit from a parkway lodged way out in Low Moor or Laisterdyke but would if a faster & higher capacity service became available via a central station. Furthermore, and largely ignored by many are the North <> South traffic flows through Bradford, which often bring the road network to a virtual standstill. With better connectivity between the two via a central station, at least some might be tempted out of their cars and onto any new capacity thrown up.
Of course all of the hinges on there being a central station in the first place, an idea that sadly passed councils and governments by for the best part of a decade. Whilst there was a ruddy great hole in the city centre, there was as close to a straight alignment between the Calder & Aire/Wharfe lines as you could wish for, albeit with a gradient issue. For a number of years a group of businessmen in the city lobbied both local and central governments hard to float the idea of a link between the two stations, with an eventual view to creating a single central station in the vicinity of what is now The Broadway. They even engaged with the then owners Westfield to look for a joint venture of station & shopping centre, perhaps with a larger footprint so as not to lose retail & parking space. I believe that they got so far as to come up with an initial estimate of something like £700M, which for what it is sounds a lot but in the wider context of a new Manchester-Bradford-Leeds alignment might actually have represented good value, particularly as a considerable amount would have come from the site owners (in the end Meyer Bergman raised £240M to build what is now The Broadway, with subsequent further investments for additional facilities along Broadway itself).
But as we know nobody was prepared at the time to commit to pushing a business case and seeing if the money could actually be raised. As with a lot of public projects in the UK, there was lots of procrastination about who was going to pay for it (without as mentioned actually floating the idea), what value it would bring, who would use it and why did Bradford need it anyway? Yet as we now see, it would have provided an ideal opportunity to realise TfN's idea with the alignment passing through Bradford, Shipley (with a possible chord bypassing the station for some services), and along the Aire line where it would have been possible to 4 track as neither Apperley Bridge or Kirkstall Forge had yet been built. So by the time the idea actually comes into the view, the opportunity has long since been lost. Once again an idea is lost as the UK shuffles uneasily towards the solutions, and by the time it reluctantly agrees to it when the ideal opportunity has again been lost.
