Can you ICAO-PPL train in an LSA?
Also, despite the steep decline in the IMCR numbers in recent years, IMHO schools will not want to lose the capability to fly IFR. Instrument training is a pretty lucrative business if you can get some. Even though most instrument training is done in actual VFR, the moment an instructor pops into a cloud and the student writes about it on some pilot forum, the school is going to be worried.
I see the LSA route will appeal to most owners, but not all because, currently, officially, getting out of the UK is not exactly simple, and some of the people spending this kind of money will want some instrument capability.
Especially if the IMCR survives and/or EASA introduces something like it elsewhere.