There are schools in the UK that offer the option of completing IR solely on the aeroplane. Whether it is a good idea or not depends on the design of the course and the fidelity of the FSTD that would otherwise be used. For example, whilst it is only a procedures trainer, an FNPT II that is precisely matched to the aircraft is a better prospect than one that is configured as a different type - if the FSTD were configured as a BE-76 when the aircraft is a DA-42 it might well be better to do the whole course on the aircraft (except for limited panel UPs, of course).
Also, with the advent of PBN and the current scarcity of approved LPV approaches, it will be difficult (although not impossible) to cover the entire syllabus in the aircraft. Of course, this issue will fade as more airfields introduce PBN procedures.
ersa - I think (hope) that you meant to say that burning holes in the sky is counter-productive.