On acquiring an aircraft for my own PPL training and later use I know that this matter has already been discussed in several other questions but the aircraft under consideration were almost exclusively Piper Warriors or a Cessna 172s which are 40 year old designs and heavy on fuel consumption.

Instead, I am considering light sport aircraft such as a Blackshape Prime or a Sling 2, for instance. I'd prefer a Blackshape Prime fitted with a CSU.

As I am still half-way towards obtaining my PPL, my question would be the following one: would it financially and technically (from a skill-set building perspective) make sense to acquire such an aircraft and lease it back to a school to do my training?

One of the school at my airport has two Sling 2 aircraft and they're quite popular with students. Most Warriors and 172s are now in their 3rd or 4th decade and seem to have run their course. Financially, in Australia, the dual hourly rate on a Piper or 172 is in the AUD 360 - 400 range, which includes AUD 100 for the instructor whereas dual rate on a Sling 2 is just about AUD 280, which makes it much more attractive to students and at no extra expense to the school.

Would it therefore be a good idea to buy a sport light aircraft such as those mentioned and lease it back to the school? Am I missing anything that is specific to them that still makes learning in Warriors and 172s relevant? Thanks for your inputs.
Is it possible? Sure. But there are pitfalls you need to be aware of...

First, you may find it difficult to find financing for a new(er) aircraft especially if you are still a student, and especially if you are intending to offer it as a lease-back. 

Then there is insurance, which for a student purchaser is going to be expensive, and even more so if you are leasing back with the idea of it being used in a flight school as a primary trainer. 

The AOPA has a good article on leasebacks:

Lenders Leery of Leasebacks
AIrcraft Owners Guide to Aircraft Leasing
Turning the tables on leasebacks

Along with any number of other articles.

Another thing you need to keep in mind is that when you put an aircraft on leaseback, you, even as the owner, are subject to the same scheduling issues as renters. 

The biggest thing to remember is that buying an aircraft for use in training is not a way to save money, you would be surprised at what it costs to own an aircraft, even on leaseback. You have annuals, maintenance, insurance, etc.