Actually we did have for couple of decades I think, if I remember correctly, it was from Lahore going south somewhere near Multan. But, the public sector babus messed it up, one side was electrified but the other side wasn't lol, I honestly do not fully remember why, but it was very poorly planned, but it did run for a long time. In the end, I think they had enough and it was closed down. So, technically don't have one right now, it was there.
I agree, there fat chance of this going anywhere right now, but remember, no matter how poor Pakistan may be, it is a large country, with size you automatically gain leverage and need for projects that would not be feasible when you are poor and small. That is basically India's story, it was and still is poor, only due to its size, it has been able to develop. It only requires few years of right policies, and few more years to stay on the path of economic growth to turn things around.
Historically, Pakistan was the richest large country in South Asia, on a per capita income basis, despite starting out dirt poor. India only retook the lead around 20 years ago and Bangladesh couple of years ago. Things are changing extremely quickly already, with terrorism largely under control, CPEC under way, and right policies already being put in place, that requires time and a bit of pain.
Plus, exploring these projects is also building understandings, and it builds the confidence of the people, and creates more space about positive news to permeate in society, where, previously there was only space for negative news. It is very much a doable project, depending on right timing, in my estimate 10 years is a realistic timeframe for mature serious discussions, and construction to start in the 2030s, to be fully operational around 2040. By 2040, Pakistan's population will likely be anywhere between 320 million to 340 million, and much of Pakistan's population is concentrated along the Karachi to Multan to Lahore to Peshawar route. So, not doable now, but worth looking into on a serious basis, after all, these projects take time and you also learn so much while making serious enquiries, and work out the suitable timeframe for when the local conditions will be ready for such a project. Such an approach saves time, and develops understanding and knowledge.