Worth pointing out that any separate spur for the Airport would mean any train running on the Leeds - Horsforth corridor serving the Airport would be doing so at the expense of Harrogate/ Knaresborough, which is quite an Opportunity Cost.
If Leeds-Bradford was a prestigious airport with four runways and hundreds of lucrative business flights then I could understand your frustration.
Instead, it's the airport equivalent of a two platform train station with only a plastic bus shelter for facilities, which is why there's not a rush to build anything.
https://insideflyer.co.uk/2018/01/what-are-the-busiest-airports-in-the-uk/
- Heathrow: 75,991,000
- Gatwick: 43,686,000
- Manchester: 26,018,000
- Stansted: 24,365,000
- Luton: 15,002,000
- Edinburgh: 12,471,000
- Birmingham: 11,832,000
- Glasgow: 9,392,000
- Bristol: 7,721,000
- Belfast International: 5,315,000
- Newcastle: 4,883,000
- Liverpool: 4,782,000
- East Midlands: 4,708,000
- London City: 4,540,000
- Leeds Bradford: 3,669,000
- Aberdeen: 2,951,000
- Belfast City: 2,647,000
- Southampton: 1,982,000
- Cardiff: 1,347,000
- Doncaster Sheffield: 1,296,000
Even if 10% of passengers used the train that'd only be five hundred departing passengers per day - not worth a dedicated branch (when passenger numbers on the Harrogate line require more services to Harrogate).
LBA exists mainly for "low cost" flights to the usual resorts and a few city breaks - if it was a proper/ big airport then there wouldn't be the requirement for Leeds to have a half hourly service to Manchester Airport.
Instead, a station on the existing line makes a lot of sense as it'll be used by commuters from the leafier places north of Leeds that don't currently have access to the train (Otley and whatnot), so serves two markets. Quite clever, I reckon. A dedicated Airport branch for such a lightly used Airport would be a waste. If you can serve it with a station on the Harrogate line then fair enough though.