I understand why people saying spending £200m isn't the wisest investment in the world - particularly with Slade Lane and the Airport Line being very limited in terms of tph. As such you're clearing a bottleneck but with little benefit on top of that.Platforms 15 and 16 would basically reduce demand for 1-12 because of Slade Lane having a limit of 22tph. While that would be useful for train lengthening in the medium term, in 2033 it will be excessive. Maybe a couple more services will run from Glossop or Marple / New Mills. As things stand 15-16 add flexibility and resilience but don't really add extra capacity unless Stockport services are diverted away from Slade Lane. I know its not a popular thing to say on here but 15 and 16 are not necessarily a good way to spend £200m.
What I think platforms 15 & 16 give you is resilience - not capacity.
If a people are taking too long to disembark and embark on the train, then the train behind can be filtered into the other platform. Having seen first hand the chaos on platforms 13 & 14, the time it takes for this process is too long - particularly on the end-door only units such as the Sprinters.
Having trains backing up to Oxford Road, Deansgate, Castlefield Junction because of effectively one train blocking the line at Piccadilly seems daft - I think for £200m it's right to be sceptical but after a few years of the problem remaining you'd eventually go "right, just build the new platforms because this problem is never going to go away". All those delayed minutes stack up and impact on the network. Extrapolate that over the course of the year and you would get you millions back over the next few decades. Would add making marginal gains is important. Having purpose built trains suited for a quick throughput with double doors would be a good start!