the northern franchise was flawed from the very start of private sector ownership financially- although very small both regional railways north east and north west made a profit (fact) north west spent their profit upping the line speed Chester to Crewe & north east used theirs to provide the loop at Dewsbury.
passenger numbers have risen massively every year since privatisation, yet arriva required a £769m subsidy until mid January when they defaulted on their franchise agreement.
My recollection is a bit different.
NWT was quickly into financial trouble and had to be bailed out by First Group (forming FNW).
MTL made a pig's ear of Northern Spirit and had to be bailed out by Arriva (forming ATN) along with Merseyrail.
The infrastructure improvements you mention were down to Railtrack as a hang-over from BR plans and had nothing to do with the private TOCs.
The franchise just ending was supposed to sharply reduce the subsidy of the former Serco-Abellio operation but they didn't get close to the target.
Remember the DfT officials said the 2015 franchise could not afford new trains, but they were overruled by the Sec of State to ensure the removal of Pacers.
That will have locked in significant extra cost/subsidy.
And all this ignores the "do nothing" decade when Labour was in charge.