The whole thread is full of "ifs". Sunak cancelled HS2 north of Birmingham because it was not value for money in the current economic climate. This proposal for a completely new line via a roundabout route has even less potential benefit but is also likely to cost vast sums of money that the UK does not have.
However, it is reasonable to spend a little money to make modest improvements to the infrastructure and passenger services on the 2 existing direct rail lines from Liverpool to Manchester.
Despite its modest network of international scheduled routes, Manchester Airport remains primarily an airport for outgoing holiday flights to the Mediterranean and other tourist destinations. Its further development is unlikely to bring major economic benefits, so the proposed devious route of this new line to serve a station near (but not at) it, is unwarranted.
Vs a do nothing option then you're probably right.
However, there comes a point where more capacity between the two cities is needed, then you're no longer at do nothing but doing something.
Minor upgrades aren't going to make much of a difference and so whilst cheaper might not gain you the capacity you need.
If options like widening the M62 or building a new motorway start being discussed then the costs of those would be quite a chunk of the new railway and would require other road improvements.
The risk is looking at what travel is like today and saying we don't need it, the thing is this railway isn't likely to open for around 5 years and probably is looking at 10+ year horizon for being useful.
Even if we assume travel demand of 1% per year in 15 years time traffic on the M62 would have increased from 90,000 to 105,000. That's about 5,000 vehicles and hour in the peak in each direction. A 3 lane motorway would likely to be congested at (or slightly below that) volume of traffic.
A fourth lane would get you another 20 years of growth at 1% until congestion was similar.
A railway line delivering an extra 10tph with 600 seats per train could have seated capacity of 6,000 (which is more cars than a 3 lane motorway can cope with and whilst cars have an average of 1.5 people it's unlikely that those cars with 3+ people would switch to going by train so the average is likely to be closer to 1).