The principle of analysis according to intention to treat is that the randomised groups are comparable, i.e. samples from the same population, and any selection post randomisation makes the groups potentially not comparable, i.e. they may no longer be samples from the same population.
From this viewpoint, both "full analysis set" and "per protocol" samples are not comparable, if any randomised participants are not included.
The first problem with intention to treat is that we need data on all participants, very difficult to achieve in medical trials. We can allow for missing data using methods such as multiple imputation. but these rely on uncheckable assumptions about the data, such as that all missing observations are missing at random. The second is that departures from the randomised treatment may lead to an underestimate of the treatment effect. The latter is the argument for FAS and PP approaches.
Personally, I would not use the FAS or PP approaches as being fundamentally flawed, since selection may have made the samples non-comparable. John and I have disagreed about this in the past. But you may find it difficult to convince your collaborators of this purist position.
Martin